The Turkish Super Lig giants were reported to have offered Balotelli a lucrative contract, with the striker likely to be on the move again after a turbulent first season with Brescia.
Brescia president Massimo Cellino revealed in May he expected Balotelli to leave his hometown club at the end of the season as the 30-year-old "no longer has his head with us".
Cellino's comments came following reports the former Italy frontman failed to attend training, claims which were denied by Balotellli before Brescia suffered relegation from Serie A.
Cebi suggested Balotelli's name cropped up when transfer targets were discussed, but Yalcin does not want to take the former Manchester City man to Istanbul.
Cebi, quoted widely by Turkish media, said: "Sergen Yalcin does not consider Mario Balotelli as one of his options for the striker position. He told me that.
"Executives usually have initial talks with players and listen to them. This doesn't mean that a move is bound to happen.
"We will make the signings Sergen Yalcin has asked of us but, I want to put it frankly, we will not compromise our financial situation."
As well as Cellino's criticism of Balotelli, the Italy international was reported to have clashed with former head coach Fabio Grosso at Brescia's training ground in November.
He was given permission to leave the club in January, only to stay put before the coronavirus pandemic caused the suspension of the season in March.
The Turkish Super Lig game was halted after four minutes and 17 seconds on Sunday for the pitch to be cleared of donations for youngsters who survived the natural disaster.
Supporters made the gesture at that time of the match to mark the time the first quake struck at 4:17am on February 6.
Besiktas said in a statement: "To boost the morale of children affected by the recent earthquakes, Besiktas supporters organised a unique donation event called "This Toy is for You" to be held at Vodafone Park during Besiktas’ match against Antalyaspor.
"At exactly the 17th second of the 4th minute of the match, which corresponded to the time of the first earthquake, Besiktas supporters threw scarves, hats, and plush toys on to the pitch.
"The goods will be delivered to the children living in the earthquake-hit areas with Besiktas aid trucks."
More than 50,000 people, including Hatayspor winger Christian Atsu and Yeni Malatyaspor goalkeeper Ahmet Eyup Turkaslan, died following the earthquakes.
Defending champions Galatasaray, Fenerbahce and Besiktas have dominated Turkish football – the three Istanbul giants winning 54 league trophies between them.
But the powerhouse trio were unable to compete with fellow Istanbul outfit Basaksehir this season.
Basaksehir – formed in 1990 – became just the sixth club to win the Super Lig since the league's inception in 1959 thanks to Sunday's victory and second-placed Trabzonspor's 4-3 loss to Konyaspor.
Boasting the likes of former Real Madrid and Manchester City forward Robinho, Gael Clichy, Martin Skrtel and Demba Ba, Okan Buruk's Basaksehir are seven points clear atop the table with one match remaining.
Basaksehir are also on track to meet Premier League giants Manchester United in the Europa League.
The Turkish champions hold a 1-0 lead over Copenhagen heading into the second leg of their last-16 tie, while United defeat LASK 5-0 prior to the coronavirus pandemic.
The Europa League is set to resume next month following the enforced break due to COVID-19.
