The Celtic boss was linked with a series of players in the lead-up to the transfer window opening and after the 1-0 win over Partick Thistle at Parkhead on Wednesday, he was asked about one of them, Wolves striker Leigh Griffiths.
The former Hoops skipper was happy enough to speak about his desire to see midfielder Joe Ledley, who scored the only goal of the game against the Jags, and Georgios Samaras, sign extensions to their respective deals which run out at the end of the season.
However, he was less open about possible new faces, although he stressed that he will be doing everything he can to bring players in.
"That (Griffiths) is just speculation," said Lennon.
"I am going to get names thrown at me all month now but I am not going to name names.
"It is a long month, it has just begun and I am being asked questions already. I will probably be doing this for 31 days
"But I am determined to bring players in to make the squad better for the latter half of the season to give some of the players here, who have been magnificent for us this season, a hand, and to make us better.
"We are in a decent position financially, where we can look to bring players in. There is no question of that.
"If we pick up a couple of injuries the squad looks light - for us.
"In comparison to other teams in the league we are still very strong but in terms of where I want to take the team and the club forward, we need an injection of quality and that takes a bit of money."
Ledley's first-half strike extended Celtic's unbeaten league run to 19 games and kept them 11 points ahead of second-placed Motherwell in the Scottish Premiership with a game in hand over the Steelmen.
Despite cruising their way to their third consecutive title, skipper Scott Brown insists Celtic "don't need motivation" for the rest of the campaign.
"We want to keep winning between now and the end of the season," he said.
"It's not easy. Look at Thistle, they came here, had a go and didn't just sit back. It was a big win for us.
"It's been a busy period for us and it was always going to be a hard game.
"But at the end of the day, three points is three points."