The 2015-16 Premier League champions are on the hunt for a new leader due to Craig Shakespeare's dismissal.
Roberts believes that the vacancy at Leicester could force the Welshman to contemplate a return to club management.
"Would Chris be interested? I think he would," Roberts told BBC Sport. "It's coming toward the end of his contract with the FAW. He's made no secret that he wants to get back into club football, but Leicester's a good club.
"I had three happy years there, very passionate fans. They've got a great owner who will back the new manager. Of course I'd be so disappointed to see Chris Coleman leave the Welsh camp, but I could understand him going to a Premier League club."
The 47-year-old has previously coached Fulham, Real Sociedad and Coventry City.