The Greece international has four years left on his contract at the capital club, but talk of Chelsea triggering Manolas' buyout clause, rumoured to be in the region of €38 million ($50m/€43m), has risen again.
But Monchi insists the 27-year-old is happy at Roma and has no desire to leave, and has had no contact from London.
"I've spoken to Kostas three or four times, he enjoys my job and might make a decent director of football himself!" Monchi said.
"He's happy with the team and wants to stay. I've read that Chelsea want to pay the buyout clause, but I haven't heard anything. I feel calm."
Monchi also dismissed the speculation around star goalkeeper Allison, who has been linked with a move to Real Madrid and Liverpool, saying there have been "no offers" for the Brazilian.
Roma have had a busy summer already. Eusebio Di Francesco’s team lost Radja Nainggolan to Inter on Tuesday, but signed Davide Santon and Nicolo Zaniolo from their Serie A rivals, while Javier Pastore joined from Paris Saint-Germain. The Giallorossi had already landed Justin Kluivert from Ajax and Ante Coric from Dinamo Zagreb.