Cullen was not involved as Pools were held to a 1-1 draw with Sutton United at the Suit Direct Stadium, after Tom Crawford’s equaliser cancelled out Joe Kizzi’s opener, with his most recent appearance coming as a late substitute in the victory over Barrow.
Cullen has made 27 appearances in total this season scoring six goals following his summer move from Port Vale.
But following the arrivals of Omar Bogle and Marcus Carver in the January window, the 29-year-old’s opportunities appear limited with Lee conceding the striker may move on from Pools in the coming days.
“There’s been a bit of movement,” admitted Lee.
“The situation is if some people get disappointed with not being involved and they’ve got an opportunity where they want to go and play some football then I’ve said to them I’ll never push anyone out.
“I want them involved in this squad but if it’s something where they feel as though they’ll be happier somewhere else then we’ll sit down and have the discussion.
“There’s been a few discussions gone on with that and a bit of movement and Monday or Tuesday will probably tell us where we are.”
Despite there being interest in Cullen, Lee retained that Cullen’s exit is not confirmed yet while admitting anything can happen in football.
“Football changes at the drop of a hat,” said Lee.
I lost three players for today but we’ll see in the next couple of days what comes about.”