Mata has enjoyed a fine season at Manchester United under Jose Mourinho.
The Spain international has featured prominently under the Portuguese, who sold him during his time at Chelsea.
He was expected to be one of the biggest casualties when Mourinho succeeded Louis van Gaal last summer, but has proved his worth with 10 goals and four assists across all competitions.
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However, the Red Devils are reportedly determined to sign Talisca, who has flourished at Besiktas on loan from Benfica this season.
And Turkish newspaper Fanatik claim Mata could end up leaving Old Trafford as a result.
It is said that United can land their man by matching his £21million release clause at the end of the current campaign.
Manchester United are targeting Anderson Talisca
As a result, Talisca's exit could pave the way for Mata to join Besiktas as his replacement.
The Turkish giants are supposedly keen to sign the former Valencia star, who will have just a year remaining on his current deal.
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Talisca, meanwhile, has scored 11 goals and weighed in with six assists this season.