Sanchez, United's highest-earning player, has failed to justify his hefty salary since joining on a free transfer from Arsenal in January 2018.
Solskjaer had recently expressed confidence that the Chilean would stay at Old Trafford beyond the close of major European transfer windows on 2 September.
But the United manager confirmed after a 1-1 draw with Wolverhampton Wanderers on Monday night that Sanchez could be allowed to leave if an acceptable offer is received.
"There's still a couple of weeks left of the transfer window and there is a chance," he said.
Rashford reveals all
Pogba missed United’s second-half spot-kick in a 1-1 draw at Molineux, with his effort saved by goalkeeper Rui Patricio.
It was the fourth penalty that Pogba has missed since the start of last season after failing to convert against Burnley, Everton and Southampton last term.
Rashford, meanwhile, has a perfect penalty record for United and scored from the spot to break the deadlock against Chelsea last weekend.
Ole Gunnar Solskjaer, the United manager, said that neither Pogba nor Rashford are designated as his taker.
Instead, the players are encouraged to decide between themselves, depending on who feels confident that they will score.
'VAR at its best'
Jesus' goal against Tottenham was disallowed after a VAR review spotted that the ball had deflected to him off the hand of City defender Aymeric Laporte.
Under changes to the laws of the game which took effect from June 1, any use of the hand which leads to a goal or a goalscoring opportunity will be penalised, whether intentional or otherwise.
There was some criticism of the decision, but former Liverpool defender Carragher believes the technology did its job.
"I think VAR has taken some unjust criticism," Carragher told Sky Sports. "I think in some cases it has been absolutely fantastic and a massive success and that was evident in what happened in the last minute at Man City.
"VAR was brilliant on this. If people have got a problem, it is with the law. I personally think handball should be disallowed if the person scores with the hand, not sets one up. But it is there in law. So that is VAR at its best.
Sokratis on Arsenal new boy Luiz
Greece international Sokratis joined last summer but despite some good performances he struggled to help improve an Arsenal defence which again proved to be their Achilles heel.
The no-nonsense 31-year-old will now be hoping to develop an understanding with Luiz and feels their contrasting styles could help form a similar to bond he enjoyed alongside Hummels during their three seasons together in Germany.
“I have known him for a lot of years,” Sokratis said of his new team-mate. “He also speaks some Greek and is a very good guy. I am happy also that we took a player like him, with experience.
“When I was in Dortmund I played with Hummels, who has the same style as David. It was also a very good partnership and it is very good (now with Luiz).
“It was his first game, it is important that we won and we can go from here.”
Sarri suffering from pneumonia
Former Chelsea boss Maurizio Sarri is suffering from pneumonia, his current club Juventus have confirmed.
The Italian, who left Stamford Bridge for Turin in June, underwent tests after being forced to sit out a training session on Monday due to persistent flu symptoms.
Sarri was not in attendance for Juve's final pre-season friendly at Triestina on Saturday.
"Maurizio Sarri, after having observed rest over the weekend, was at the JTC Continassa today where he coordinated the work of his staff," read a statement issued by the club, who begin their Serie A campaign at Parma this weekend.
Pochettino calls on Premier League to change rules
Tottenham Hotspur boss Mauricio Pochettino has called for the Premier League to bring its summer transfer window back in line with Europe's major competitions.
A majority of English top-flight clubs - including Spurs - voted two years ago to move transfer deadline day, previously at the end of August, to a date before the season began.
The reasoning at the time was that some clubs felt unsettled by the potential disruption of player moves during the early weeks of the campaign.
Pochettino claims this has not worked because, with no uniformity across the continent, clubs can still lose players to European sides even after the domestic deadline has past.
Spurs are feeling that particularly this year with a number of players now into the final year of their contracts - notably playmaker Christian Eriksen - being linked with moves elsewhere.
Wolves fans vent fury with VAR
Thousands of Wolverhampton Wanderers supporters howled a well-known four-letter word at VAR on Monday while their team's manager pleaded for a solution to prevent the video review system sucking the passion out of Premier League football.
Making its debut in the English top flight this season, the Video Assistant Referee system deprived Wolves of a goal against Leicester City in their opening 0-0 away draw.
The Molineux faithful made their disparaging views on VAR abundantly clear during a heart-stopping couple of minutes in Monday's 1-1 draw at home to Manchester United when play was stopped to check on Ruben Neves' second-half equaliser, with chants of “F*** VAR” filling the Wolverhampton air.
Though the goal was allowed, and a possible offside by Joao Moutinho discounted, Wolves manager Nuno Espirito Santo still fretted afterwards that VAR was killing the game's passion.
"What I'm afraid is we will be afraid to celebrate the goal," he said.