The English Championship side reportedly submitted an offer in the region of £1 million last month for McGinn, pictured.
Lennon, who is running the rule over former Liverpool and Arsenal winger Jermaine Pennant, said: “We had an offer from Ipswich and it was nowhere near the valuation we have of the player and that’s the end of it.”
While Lennon is keen to keep his prized assets, his immediate focus is on building a squad for the club’s Premiership return.
He is hopeful of bringing back Scotland defender Steven Whittaker to the club following the player’s release from Norwich City.
The former Celtic manager has also refused to rule out a move for Blackburn Rovers striker Anthony Stokes, who scored two goals while on loan at Hibs in their Scottish Cup final triumph over Rangers last year during his second stint at Easter Road.
On Whittaker, Lennon added: “We’re in talks with Steven and we’re hoping to get closer in the next few days.”
Asked about Stokes, Lennon, who confirmed a move for Cambridge United midfielder Luke Berry “is off”, replied: “It’s speculation, he’s a Blackburn player. Until we get the player in the building and signed, nothing is definite.”