Fulham are believed to have failed with two offers for the 27-year-old in recent weeks, but there is still a chance that the Scotland international could leave Old Trafford before the market closes for business.
Napoli are said to be one of the clubs showing an interest in McTominay, with Man United's asking price for the midfielder thought to be around £25m.
The Italian outfit are also being heavily linked with Brighton & Hove Albion's Billy Gilmour, and Manna addressed the transfer talk before Napoli's Serie A clash with Hellas Verona.
"They [McTominay and Brighton's Gilmour] are good, strong players. Let's see what happens in the next few days. It's useless to make forward momentum today, there is the game and after the game, we will think about the market," Manna told reporters.
McTominay 'emerges' as transfer target for Napoli
McTominay has been used off the bench in Man United's two matches this season against Manchester City and Fulham in the Community Shield and Premier League respectively.
The Scot has entered the last 12 months of his contract at Old Trafford, and although the club have the option to extend it for a further year, it is likely that he will be allowed to leave if a suitable offer arrives.
McTominay came through the youth system at Man United, and he has represented the club on 254 occasions, scoring 29 goals and registering eight assists in the process.
Last season, the midfielder scored 10 times in all competitions, but he is down the pecking order for the starting roles in the middle this term, and Paris Saint-Germain's Manuel Ugarte could soon arrive to further boost Erik ten Hag's midfield options.
Ten Hag said last month he wants to keep McTominay
"I think we have very good players so they'll always have an interest from other clubs," the Man United boss told reporters last month when asked about McTominay's future.
"If you score 10 goals in a season and perform very well for Scotland there will be an interest. We want to actually keep him because he's a very important player for our squad.
"We've seen what he can contribute last season. When we had the sixes and he could play in a more advanced role, he's a highly interesting player for our team."
However, a switch to Napoli would represent a wonderful opportunity for McTominay, as he is unlikely to receive the number of starts that he will be looking for this season at Man United.