The Chile international moved to Manchester United in a swap deal from Arsenal in the January transfer window.
Sanchez arrived at Old Trafford as one of the best top performers in the Premier League during his three and a half spell at Arsenal.
The 29-year-old only managed to score three goals in 18 games in all competitions during the second half of the campaign.
The South American has failed to find the net in the opening six games of the current season to ask further questions of Sanchez.
Former Chelsea FC defender Burley believes Sanchez needs to be sold despite arriving at Manchester United less than nine months ago.
“Sanchez is not a good fit for Man United,” Burley told ESPN FC. “They may as well look to sell him.”
Sanchez won two FA Cup crowns during his spell at The Emirates after the South American winger moved to Arsenal from FC Barcelona in a 35m deal in 2014 summer transfer window.
The Chilean forward has never won the Premier League title during his spells at both Manchester United and Arsenal.
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