The Black Eagles are trying to scoop up Alli and it was recently claimed Everton are open to letting him leave either on loan or on a permanent transfer.
Besiktas want to loan Alli, with an option to buy, and according to Turkish daily Takvim, they expect him in Istanbul today for his medical as they have an agreement in place with Everton.
It is claimed that Besiktas will take Alli on loan and have an option to buy in the deal.
The buy option will be set at €8m, but if Besiktas trigger it in January then they will only have to pay €6m to sign him permanently.
If Besiktas wait until the end of the season to trigger the option then they will have to pay Everton €8m.
Alli has failed to make an impact at Everton since joining the club from Tottenham Hotspur in the January transfer window earlier this year.
The midfielder has seen his stock fall rapidly in recent years and could now be set for a switch to Turkey, linking up with a side that finished sixth in the Super Lig last term.
