After signing Nana from Peterborough earlier in the week, Cobblers boss Gary Johnson may return to London Road for Welsh international Davies, surplus to requirements following Posh's promotion to the Championship.
Director of football Barry Fry has hinted that he expects the player to link up with his former manager this summer.
“People at a higher level might not be ready yet to come down to this level but there are ones out there that I think we’ve got a pretty good chance of bringing in," said Johnson, quoted in the Chronicle & Echo.
“I’m not worried about it. I think we need probably four or five to come in and I’m pretty happy we’ll have all of those in place before the start of pre-season."