Man enjoyed a breakthrough season for Steaua during the 2017-18 campaign, making 47 appearances across all competitions and establishing himself as a first-team regular for the Romanian club.
The youngster's form has also seen him break into the Romanian national team, and Steaua president Gigi Becali has put an asking price of £26m on his head in an attempt to ward off interest from Jose Mourinho's side.
"Manchester United asked me about Dennis Man and I want €30m (£26m)," Becali is quoted as saying by The Mirror.
"I know that they won't pay this amount, but the player isn't for sale."
United manager Mourinho is understood to have watched Man during Romania's 2-0 win over Finland this week.