Turkish club Galatasaray had confirmed before Saturday's game against Osmanlispor that the 27-year-old was the subject of foreign interest: "Badou Ndiaye has received offers from clubs overseas".
It came after the Senegalese was left out of that league match after allegedly pleading with the club management to let him depart amid interest from the Premier League side.
The statement also said: "Badou has been removed from the squad set to face Osmanlispor as he is currently distracted from his on field duties by the transfer talks".
The English newspaper have also reported on Sunday that Stoke have already made a £14m bid as they face competition from Crystal Palace, West Hame and Newcastle United.
Ndiaye has made 16 appearances for Galatasaray this season after joining from Osmanlispor in the summer and would join Kostas Stafylidis as Lambert's second January signing.