Hawthorn announced on Saturday that Franklin had put off contract negotiations with the club until the end of the season, when he will become a restricted free agent.
Wells, who has played 190 games for the Kangaroos over 10 seasons, becomes a free agent at the end of this season too.
But Wells told the Herald Sun he wanted to stay at North.
"I would love to be a one-club player," Wells, who turned 28 on Sunday, said.
"I would love to see out my career with them. Hopefully I still have plenty of years, so I will just get out on the park and play good footy, and that will take care of itself.
"I have got a lot of time for the Kangaroos. We have been through some tough times but we are a really good team and it's exciting to be part of and I want to help the young ones out."
Wells has endured another injury-interrupted pre-season this summer, with the after-affects of an achilles strain in round 20 last season limiting his training workload.
But North said last week Wells was on track to play in some of North's NAB Cup games, having recently recommenced competitive training.
Wells, too, has been buoyed by the recent improvement in his achilles.
"I played (in the session on Friday at Geelong) and got through the whole session and I am moving pretty well," Wells said.
"I didn't have surgery but [my achilles] was really sore and tender pretty much the whole time [at North's November training camp] in Utah, and it was frustrating, but I tried to make sure no one picked up on my body language.
"It still wasn't quite right when I got back to Australia, but in the last couple of weeks it's gone pretty well and now we are putting heavy loads into it.
"The 'docs' have assured me it is going to be fine, so I am getting some run in my legs."
Nick Bowen covers North Melbourne news for AFL.com.au. Follow him on Twitter: @AFL_Nick
