Former Ibrox director Dave King, who lost £20million at the Govan club during a previous regime, is looking to effect change at Rangers with a fresh share issue, and 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 claim 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 the Parkhead club in the league.
However, ahead of the Scottish Premiership clash with Partick Thistle on Wednesday night, where Celtic could clinch their third successive title if Aberdeen drop points against Ross County on Tuesday, the Hoops boss 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 or should 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 was speaking at the club's Lennoxtown training complex four years to the day after he was named as the Hoops' interim manager, following the departure of Tony Mowbray, before taking the job on a permanent basis.
The former Parkhead skipper recently revealed in an interview that he wants to manage in England in the future, adding that he was disappointed not to have yet received any offers.
However, he admits considering a position like the one at his former club Nottingham Forest would be difficult due to the owner's demands, which were alluded to by Neil Warnock when he rejected the opportunity to take over at the City Ground from Billy Davies.
The former Crystal Palace, QPR and Leeds boss said: "I wanted to keep my own direction. If I can't go into something 100 per cent manager, as I like to manage, I cannot commit to it."
It was in the context of boardroom interference that Lennon said: "It is a very difficult thing to do. Where does that leave your position of strength at the club?
"That would make my position certainly not enjoyable and probably untenable.
"I understand why Neil didn't take the job. Some owners come in and I am not sure that they understand the environment.
"I think the Championship is such a competitive division. There is a certain way of playing to get results and that may not be conducive to the way some owners want the game to be played.
"I think owners come in and have the right intentions. I think they are sometimes a little bit misled.
"I think that is the way the game is going, unfortunately."
Lennon stressed that he is in "a fantastic position" with regards the board at Parkhead.
He said: "I have a great board and great people in the background who give you great advice.
"We are in a difficult economic situation at the minute but certainly the way the club is run and the way I am treated, you couldn't ask for any more really."
The Northern Irishman expects Thistle to be desperate to stop a title party if Celtic do have the chance to clinch the title.
Lennon, who will watch the Manchester derby on Tuesday night while keeping his ears open for news from Dingwall, said: "They have their own self-pride and pride in their club.
"And 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.
"We will wait and see what (Tuesday night) brings but the players and myself are looking forward to the Thistle game.
"It is midweek, a full house, a local derby and that is enough to whet the appetite.
"We are playing very well at the minute and I would like that to continue."