The 30-year-old joined Tianjin on a two-year loan from Cologne in Germany last summer and hit seven goals in eight games last season.
But the forward, a regular goal-scorer in the Bundesliga before moving to China, has netted only four goals in 12 games this term and was not in the squad on Sunday for Tianjin's 3-3 Chinese Super League (CSL) draw at Beijing Renhe.
Modeste has been missing from training, the Tianjin Daily said on the eve of the game, and quoted the team's Portuguese coach Paulo Sousa as saying: "When we were at winter training in Marbella, Spain, I knew something was up.
"I tried to solve it as much as possible to have Modeste focused on training and matches and the club has been helping to solve the problem too, but so far, we have not had much luck."
French sports daily L'Equipe said Nice are interested in taking back Modeste, who played for them a decade ago, but face competition from clubs in Germany, Turkey and Russia.
Tianjin are in the knockout stages of the Asian Champions League but are toiling in mid-table in the CSL and recently lost star midfielder Axel Witsel to Borussia Dortmund in Germany.
But they still have the Brazilian forward Alexandre Pato, whose strike in Sunday's stalemate was his 10th goal in 12 league games.