Naylor, handed the captain's armband following his arrival from Ipswich in February, is currently recovering from back surgery, while previous skipper Frazer Richardson was released last month and has since joined Charlton.
Howson, 21, said: "It'd be a massive thing to be asked. I enjoyed it when I had it for a bit at Huddersfield a couple of seasons back and at York last Sunday.
"I think the gaffer will rotate it and if Nayls is back he will be captain, but if he isn't and it came my way, I'd take it, and it'd be an honour."
The Leeds-born midfielder has made nearly 100 first-team appearances since making his debut in 2006 and briefly skippered the side against Huddersfield in the absence of Jonathan Douglas two seasons ago.