The Turkish giants are pushing to sign Alli and have a private jet on standby to take him to Istanbul.
Alli though has yet to board the jet and Everton are waiting for the midfielder to accept the offer from Besiktas.
Frank Lampard’s side are prepared to be flexible on his departure and are willing to let him join Besiktas either on loan or on a permanent basis, as they try to offload him.
The midfielder appears to be surplus to requirements for Lampard, despite only having been signed in the January transfer window, from Tottenham Hotspur.
Alli has clocked just 38 minutes for Everton across their two Premier League games so far, struggling to make an impact.
He was an unused substitute in seven of Everton’s final 12 Premier League matches last term, as the Toffees fought for survival in the top flight.
Now Alli could be set to move to Turkey in another bid to get his faltering career back on track.
