Lennon also said that former Juventus midfielder Fausto Rossi has been offered a trial at East Mains, while he refused to rule out an interest in St Johnstone playmaker Danny Swanson.
Hibs have been decimated in midfield ahead of tonight’s top-of-the table Ladbrokes Championship encounter at Dundee United.
Fraser Fyvie and Alex Harris have joined Scotland international John McGinn, who underwent ankle surgery last week, in the treatment room with groin and hamstring problems respectively.
The interest in Pennant has gone as far as having a look at the 33-year-old, who has recently been playing in Singapore with Tampines Rovers, in training, while Lennon concedes he is less likely to recruit Osman.
The 35-year-old is a free agent after ending his 19-year association with Everton during the summer.
Lennon, whose side lead United at the summit by three points, said: “Fraser Fyvie will be out for about four weeks. It’s a groin tear and there’s been a bit of swelling so it’ll take a bit of time to heal.
“The two boys [McGinn and Fyvie] being out will have a bearing on the performance because they’ve been so good for us. It’s just unfortunate these injuries have come at the wrong time for us.
“Alex Harris is out for three or four weeks with a torn hamstring as well.
“We are actively looking to bring someone in at the minute. We’ve made a couple of enquiries and then in January as well we’d be looking to add to the midfield department if we can.
“Jermaine Pennant came in and trained for a couple of days and we’ve left things with him.
“We spoke to Leon Osman’s representatives as well but that was probably too ambitious from our point of view.
“It’s not like we’ve been sitting still. We are actively out there making contact with people, trying to strengthen what we already have.
“We’re not trying to get these guys in for a PR stunt. We’re trying to improve the team and help us get promoted. I’ve got a good recruitment team who work very, very hard.”
Asked about Swanson and Italian midfielder Rossi, who was farmed out on loan to Brescia, Valladolid, Cordoba and Pro Vercelli during his time at Juve, Lennon replied: “I don’t know where the Swanson story’s come from.
“It’s just come out of the blue. If I was going to make contact, the first person I’d call would be Tommy Wright. There’s been no contact there.
“In terms of Rossi, he’s not got a club and we’ve made contact with his agent, but that’s as far as it’s gone. We’ve asked him to come in and train with us for a few days but we’re waiting on confirmation of that.”
Former Celtic manager Lennon, meanwhile, has dismissed United counterpart Ray McKinnon’s theory that Hibs could crumble under the weight of expectation of trying to achieve promotion back to the top flight at the third time of asking.
Hibs drew 1-1 with United at Easter Road in October and have won four of their last five league matches.
Lennon added: “I’ve seen no evidence of that so far and I don’t know what he means by saying we could crumble. You either play well or you don’t, you either win or you don’t. If anything the pressure is on Dundee United. If they lose the game on Friday, where do they go? They’re six points behind chasing us.
“If they win, they’re still behind us so all the pressure is on them really. We’re fine. I’ve not seen any evidence of a lack of mentality creeping in.”
With a crowd in excess of 11,000 expected at Tannadice for the televised encounter, Lennon added: “And being at home, they’ll have a big crowd for the first time in a while and it will be interesting to see how they handle it.
“It’s been built up to be a big game but we’re only at the beginning of December, it’s not going to finalise or settle anything. You’ve got two teams who are in form that are first and second. In the context of the Championship it’s a big game but I don’t think the result will have any bearing on the outcome.
“What it will do is give us a chance to extend our lead at the top of the table. If we lose the game we’ll still be top of the table.”