Earlier this summer, the 26-year-old revealed that he is keen to leave the King Power, prompting interest from a number of clubs across Europe.
Despite the uncertainty, Mahrez has continued to train with the side and has pledged to give his best while he remains a Leicester player.
"It's to be expected that big clubs will be after our biggest name players," Morgan told Sky Sports News. "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 and there were no hard feelings there. We'd all love Riyad to stay, but who knows what will happen."
As it stands, Mahrez is likely to feature for Leicester when they begin the new Premier League season away at Arsenal on Friday night.