Alli only arrived at Goodison Park from Tottenham Hotspur in January on a free transfer in a bid to get his career back on track.
However, the England international has so far struggled to make an impact at Everton and boss Frank Lampard is open to letting him go this summer.
Turkish giants Besiktas have zeroed in on Alli as a marquee signing in the ongoing window and have been working on an initial loan deal for him.
Besiktas have reached an agreement with the Toffees over taking Alli to Turkey on a temporary basis, without a loan fee, but a deal is yet to be sealed.
According to Turkish magazine Fanatik, Alli is currently sorting out some paperwork issues with Everton which are delaying him from securing a move to Besiktas.
The Super Lig side are working at full speed to get a deal over the line for Alli as soon as possible, with just over ten days left in the transfer window.
Besiktas will have purchase options in the loan deal for Alli set at €6m should they wish to sign him outright in January or €8m if they want to buy him next summer.
