He revealed: "Since Lee joined us, he's been as good as gold. He's trained incredibly well. He looks as though he's enjoying it and I'd like to keep him longer.
"If we could try and get him for another couple of months on top of the current one that is something I'd seriously go for.
"If we got promotion - and there was a chance we could afford him - then Lee is definitely a player I'd look to bring in."
Having been Marshall's boss twice in the past, with the England Under-21s and at Leicester, Taylor is confident Marshall would be a good acquisition again.
He continued: "I know his pedigree. I know what he's like and I know he'd do very well for us.
"He's at a good age. He's a lot to prove but I'm sure he would get better and better."
Elsewhere, there has been a departure from the Tigers camp. Rookie forward Clayton Donaldson has joined Halifax Town - 14th in the Conference - on a month's loan, and made his debut as a substitute in their 2-0 defeat at Margate yesterday.