Roma have had an offer rejected for the winger as they seek to replace Mohamed Salah, with sporting director Monchi indicating they may not return with a fresh bid for the Algeria international.
Mahrez, PFA Player of the Season in Leicester's Premier League title-winning campaign in 2015-16, has continued to feature for the Foxes during pre-season despite announcing his intention to move on.
And Morgan says Mahrez has acted professionally, with Leicester set to get their Premier League season under way with a trip to Arsenal on Friday.
"It's to be expected that big clubs will be after our biggest name players," Morgan told Sky Sports. "But at the end of the day he is still with us.
"He is a still a Leicester player and that's all that matters. We can't think about what could happen or where he might go.
"At the training ground we all train together and I have to say is his attitude has been great. He hasn't shown that he is angry or that he is upset in any way or that his head is not in it. He comes in and he trains hard.
"We expect players to come and players to go. [N'Golo] Kante went [to Chelsea] and there were no hard feelings there. We'd all love Riyad to stay, but who knows what will happen."