The striker is one of a number of Ibrox stars in the final year of their deal.
It has been a difficult campaign for Morelos who returned from a long injury lay-off. He has scored once but he's also been sent off against Hibs and dropped for the huge Champions League qualifier with PSV Eindhoven due to not being in optimal condition.
Hutton reckons the player may have had his head turned by interest from elsewhere but is hopeful the player will show he is worthy of a new deal.
"I believe Rangers are a better team when Alfredo Morelos is in it and firing, playing with full confidence,” he told Football Insider.
"I would like to see him sign a new contract and stay. I know his head has maybe been turned over the last season and a bit. The speculation around moving to different clubs, I don’t think that’s helped him.
“Obviously after an injury last season he maybe thought as soon as he was fit he was going to start and that didn’t work out.
"We know everything that happened but he’s shown another side, that he’s willing to work hard to get back into the team.
“It’s up to him, the ball’s in his court. If he wants to fight for a new contract or go to another club, you have to be playing at a certain standard and he’s going to have to reach that to get either one."