Richardson parted ways with the Spireites only last week after they opted not to offer him a new contract having failed to gain promotion from League Two in the two years he had at the helm.
The club came close to a play-off spot on both occasions, finishing 10th this year, but it was not good enough to remain at Saltergate.
Richardson has already had an interview for the position at newly-promoted Burton Albion as he looks to make a quick return to the game, but he has also expressed his interest in what is going on at Vale Park.
"Vale should be a Championship club," he said in The Sentinel. "I don't know if I could achieve that in two years, but there are enough players out there to get that momentum going.
"I've made a decent start to my managerial career and I want to utilise my experience and energy to good effect. I could hit the ground running because I already have players in mind for next season. Vale are a bigger club than Chesterfield and have a lot of potential."