The France international has been linked with moves to both the Gunners and Spurs, but is currently going nowhere according to the man in charge of the Ligue 1 club's player sales
Despite admitting that there was still interest in the 22-year-old defensive midfielder, Dreossi claimed that the longer time went on, the less likely a move to the Premier League would be.
He also acknowledged that Rennes would like to keep hold of the player as their squad would be stronger with him in it - and said there would be a decision on his future within the week.
"There is nothing big to report. We've had some contact, but nothing more than that," he told France Football.
"The more we go on, the more we can think [that he'll stay].
"Now, as I've been saying for a long time, we will know whether Yann will eventually leave in the final week [of the market].
"If Yann stays, all the better, and we'd be a bit stronger with him than without him."