The Scottish Premiership champions were linked with making a bid for the 27-year-old.
The Scottish Sun suggested that Celtic boss Brendan Rodgers was interested in linking up with the forward once again - having previously worked with him at Swansea City - and had cemented his interest with an offer of that figure.
However, the Mail are claiming that sources at the club have disputed whether such a bid is on the table, while the report also states that new Villains boss Roberto Di Matteo has yet to decide whether the 27-year-old features in his plans.
Should he come to the conclusion that Sinclair is not one of the players that can help the Midlands side get themselves out of the Championship, the Mail adds that a similar bid to the one that has been made according to The Scottish Sun would not be accepted as Villa will hold out for a larger fee.
Like most of Villa's squad last season, Sinclair was guilty of not performing at the level he has previously proved that he is capable of reaching.
However, with the fresh optimism that currently exists following the change of leadership, both in the boardroom and in the dugout, he may be hoping to prove to Di Matteo that he can help the side go up and subsequently re-establish themselves in the Premier League.