Dunne told Sky Sports News earlier this month that he is looking for a new club due to Aston Villa manager Paul Lambert's preference for selecting younger players.
The 33-year-old failed to feature under Lambert last season due to injury and made his first appearance since Euro 2012 when coming on as a substitute in the Republic of Ireland's win over Georgia at the weekend.
Lennon acknowledged that signing Dunne would be contrary to his usual transfer policy, but conceded the centre-half's experience could be valuable.
He said: "I like Richard Dunne, I always have done. He's a great player, a great Irish player. He's had a long time out with injury and just the way we go about our business now, his age might go against him.
"However, I am not ruling that one out. He's a player I have admired for a long, long time, but I am sure there will be a number of clubs pursuing his services.
"That's a player we will think about, but in terms of the direction we go, his age would probably rule him out of that."
The SPL champions are also considering whether to make a bid for Balde, who has one year left on his contract with Portuguese side Guimaraes.
Lennon added: "Balde is a big striker and has the physical attributes we are looking for. But he is interesting other clubs as well.
"We haven't pushed the button on any player but we have a number of options in each position. What we will try to do is bring some players in for June 20 when we start pre-season training."