Ipswich are seeking to secure young midfielder Owen Garvan to a new contract.
"Owen has a bright future and we want that to be at Ipswich Town," Magilton told the club's official website. "He has progressed at the club and we want him to continue to move forward here.
"I've sat down with him and had a chat and the two-year contract extension is on the table for him.
"He knows we want him to stay here and become part of what we are trying to build at this club and he can have an important part to play in that."