Former Ibrox director Dave King, who lost £20million at the Govan club during a previous regime, is looking to affect change at Rangers with a fresh share issue, and was reported as saying he is prepared to put in another £30million in his bid to make the Scottish League One champions competitive with their traditional city rivals again.
The South Africa-based Glasgow businessman's claims came a couple of days after Aberdeen chairman Stewart Milne, celebrating the Dons' Scottish League Cup final victory parade in the Granite City, told fans that he would "do everything in our powers" to get closer to Celtic in the league.
However, ahead of the Scottish Premiership clash with Partick Thistle on Wednesday night, when Celtic could win the title if Aberdeen were to drop points against Ross County on Tuesday, the Hoops manager played down the prospect of rival clubs spending big money to force a challenge.
Lennon said: "I wouldn't imagine that would happen. I think the owners of clubs are far too astute for spending big money and trying to chase it.
"I think they will build brick by brick over maybe the course of two, three, four seasons and really try to close the gap.
"We haven't spent an amazing amount of money over the last couple of years so we still have some stock in the bank if we need it.
"But no, I can't imagine clubs like Aberdeen or Rangers at this stage, will start throwing millions of pounds at it to chase it."
Lennon expects Thistle to be desperate to stop a title party if Celtic do have the chance to clinch their third successive championship.
The former Celtic skipper, who will watch the Manchester derby tonight while keeping his ears open for news from Dingwall, said: "They have their own self-pride and pride in their club.
"They have an agenda, to avoid second-bottom place.
"They are fighting for their lives so it is a not a foregone conclusion that the title will be wrapped up this week."
Meanwhile, Celtic have no fresh injury worries for their Scottish Premiership clash with Partick Thistle at Firhill on Wednesday night.
Midfielder Nir Biton and winger James Forrest remain on the sidelines with groin injuries.
Derk Boerrigter, another wide-man, is also still out with an abdomen problem.
Provisional squad: Forster, Matthews, Van Dijk, Ambrose, Izaguirre, Brown, Mulgrew, Griffiths, Kayal, Commons, Pukki, Balde, Samaras, Stokes, Johansen, Fisher, Henderson, O'Connell, Zaluska.