Alli was loaned to Besiktas by Everton in the summer, with the Turkish side also including an option to buy in the agreement.
He was welcomed in Istanbul with much fanfare, but has failed to deliver on the pitch and Besiktas have been looking at terminating the loan deal this month.
However, according to Turkish journalist Gokmen Ozcan, Everton are unwilling to take Alli back.
The Toffees do not want Alli to return to Goodison Park in the final days of the transfer window and he is set to see out the season in Turkey.
Besiktas will be hoping that Alli can put a disappointing first half of the season behind him and start to make an impact in Turkish football.
They are ten points off league leaders Galatasaray, but with a game in hand, and are in action later today at home against Alanyaspor.
Alli has clocked just nine appearances in the Turkish Super Lig for Besiktas, finding the back of the net once, against Ankaragucu.
