The 23-year-old has been strongly linked with a return to English football, having previously played for Norwich City, after ending last season strongly with a string of goals and assists across Serie A, the Europa League and the Coppa Italia.
Bologna's stated intention remains to keep hold of a player considered central to their project, though the club would be prepared to consider a sale alongside Rowe himself should a sufficiently large offer arrive from England, with reports elsewhere putting his valuation in the region of €40million.
Chelsea are said to be searching for further attacking options on the left flank after an internal reassessment of the squad, with Crysencio Summerville, Yan Diomande and Francisco Trincao also among the names on their list, but Rowe remains one of the players Chelsea's recruitment staff continue to track most closely.
According to the report, fresh contact has taken place in recent hours between Chelsea and representatives of the player, though no official offer has yet been submitted. Bologna are aware that a serious approach from the Premier League could change the picture quickly, much as it did previously with Dan Ndoye and Riccardo Calafiori, both of whom left the club for England in recent transfer windows.
Elsewhere at Chelsea, academy defender Harrison Murray-Campbell has joined Belgian top-flight side KV Kortrijk on a season-long loan. The 19-year-old, who has been with Chelsea since Under-8 level and made his senior debut as a substitute in a Conference League win over Shamrock Rovers, scored six goals in 20 Premier League 2 appearances last season as Chelsea's Under-21s finished top of their table, and also netted the winner in a Youth League victory away at Bayern Munich.
He joins a Kortrijk side who secured promotion to the Belgian top flight after finishing second in last season's Challenger Pro League.