Magilton told BBC Sport: "I'd like to keep Ben at the club. If we can keep him until the end of the season or do a deal to sign him then I'd be delighted.
"It's something we'll leave to the money men. I definitely want him. He's a player I rate highly. He is energetic, keen and ambitious."
Watson made six Premier League starts for Wigan before Roberto Martinez's arrival, after which he was promptly loaned out to QPR in September.
However, he has been a key player for the Hoops since captain Martin Rowlands was ruled out for the rest of the season with a knee injury.