Leicester City, West Ham and Valencia all tried to sign Mohamed Elneny from Arsenal during the transfer window, according to the midfielder's agent.
Elneny swapped Arsenal for Besiktas on a season-long loan in August after falling down the midfield pecking order at Emirates Stadium.
The Egypt international was also said to be wanted by other clubs, while reports in Italy this week suggested AC Milan may make an approach in the January window.
"He received a lot of offers last summer, led by Leicester City, West Ham and Valencia, but Besiktas managed to settle the deal with Arsenal," agent Alan Nazmy told Egyptian TV channel Time Sport.
"Milan and Roma previously tried to sign the player during the last winter transfer window, but the negotiations didn't work then, and he received more than one offer as well."
Asked about fresh rumoured interest from Milan, Nazmy said: "I can't talk about it."
Elneny made 89 appearances for Arsenal in all competitions after joining from Swiss side FC Basel in 2016, including 17 outings last season.
Arsenal boss Unai Emery allowed the 27-year-old to leave following the arrival of Dani Ceballos and emergence of academy product Joe Willock, but the door has not been closed on a return next year.
"Emery didn't ask for his departure from Arsenal because of his performance," Nazmy said. "He demanded that [Elneny] took a chance to develop his performance and return again.
"It is possible for him to play with Arsenal again. It still remains a strong possibility."