Ahmet Nur Cebi, vice president of Besiktas, has said the club is "clear" about wanting Tosun to "stay on," per Emre Sarigul of Turkish-Football.
Sarigul also quoted Besiktas general secretary Ahmet Urkmezgil revealing the Blues' interest: "Chelsea sent club officials and a scouting team to watch him during the derby."
Chelsea's apparent interest means Tosun's list of suitors is growing. Earlier in December, Turkish outlet Fotomac reported Valencia, Newcastle, Everton and Juventus are also keen on the forward (h/t TalkSport).
This level of interest makes sense given Tosun's superb performances for the Black Eagles. The 26-year-old has scored 11 times and provided three assists in all competitions this term.
He was a key figure in helping Besiktas qualify for the last-16 stage of the UEFA Champions League as Group G winners. Tosun thrives in an attack that also includes Ryan Babel, Ricardo Quaresma, Alvaro Negredo and Anderson Talisca.
Tosun is also versatile enough to provide cover in a number of positions in the final third. He would give Blues manager Antonio Conte another option through the middle beyond Michy Batshuayi and Alvaro Morata.
His ability to play on either flank would also be an asset for Chelsea despite Eden Hazard, Pedro and Willian's presence. The latter has been on the fringes of the first team this season, although his recent form has persuaded the Blues not to sell the Brazilian in January, according to French source Le10 Sport (h/t Metro).
Even so, Tosun would be a smart signing for Chelsea since Sarigul noted Besiktas value the player at £30 million, a relative bargain for a skilled attacker who continues to get better.