Speculation has linked the 27-year old with a switch to Old Trafford in recent weeks as David Moyes looks to bolster his midfield, with the retirement of Paul Scholes and uncertainty over Darren Fletcher's long-term future due to illness leaving him with limited options.
Marchisio has spent his whole career with the Serie A champions, but the Italian has already admitted that he would be "very proud" if United did make an offer for him.
The midfielder is currently away with the Italy national team at the Confederations Cup, where his side have already reached the semi-finals after two opening group stage wins.
Marotta remains hopeful of keeping hold of Marchisio, who is under contract in Turin until 2017, and he says they will do their best to ensure that he stays.
"Marchisio? There is no meeting; there is no problem with him," he told Sky Sport 24 Italy.
"Juventus have never thought about putting him on the market, he is an important player and we will try to keep him with us."