Speaking on the development, the 50-year-old was quoted by the Turkish newspaper as saying: "I thank Beşiktaş for their impressive offer. I have not made my decision yet."
The former Super Eagles player signed an 18-month loan deal with the Turkish giants on Friday. The 28-year-old will remain at the Turkish side until the end of the 2019/20 season.
Away from Stamford Bridge, he also won the Turkish Super Lig, the Turkish Cup, Turkish football's Player of the Year award, and two African Player of the Year awards.
The previous year, he was sacked from the Turkish national football team squad by then-manager Fatih Terim after verbally and physically assaulting a Turkish sports journalist on a flight to a match.
It is understood that Talisca has a £20million release clause in his current deal with Besiktas but the Turkish side have not shown interest in signing the midfielder on a permanent deal this summer.
"I grew up as a @Fenerbahce fan as a kid in Germany - every German-Turkish person supports a Turkish team when they grow up in Germany. "And mine was Fenerbahce. Fenerbahce is like Real Madrid in Spain.
Turkish professional football club Galatasaray had joined Premier League side Fulham and Saudi Arabian club in the race to sign the 30-year-old Brazilian midfielder.
Trabzonspor are in contention for Europa League football next season, after their fourth-place finish in the Turkish Super Lig in the 2018/2019 campaign.
The two new-born boys have been named Recep and Tayyip, the first two names of the current Turkish president Recep Tayyip Erdoan, according to Turkish news outlet Ensonhaber.
A Turkish military helicopter with 14 people onboard has crashed in the northeastern province of Giresun. According to CNN-Turk television, among the occupants is a brigadier general. The cause of the crash was not immediately known.
It is also instructive to be forewarned against deceptive advertising of job opportunities in the Turkish Republic of Northern Cyprus" the statement read
Last weekend, Mikel Obi criticised Turkish football authorities, for not suspending the Super Lig season despite the spread of the coronavirus across Europe.