The former Celtic boss had made tying last season’s 25-goal frontman down on a new deal his number one priority after taking over at Easter Road.
He even flew the player and his agent out to Paris for face-to-face talks while working as a BBC pundit at Euro 2016.
But Lennon knows Cummings has other options and Rotherham could test Hibernian’s resolve after making contact with the Leith outfit.
That is despite new Millers boss Alan Stubbs promising he would not raid his former club for their top stars when he quit Hibs earlier this summer.
However, Lennon is confident he can persuade his ace marksman to stay put, saying: “I’m hoping to get the Cummings negotiations finished off quick. If we can, that will be another boost to the squad.
“We’re under no pressure to sell him so I’m not worried about any rumours at all.
“If we can keep him it means we’ve got a 25-goal striker in our ranks, which will be very important if we want to get out of the Championship.
“I think he’s happy here and he knows he’s wanted. I’m still getting to know him but he has an infectious personality. He has got a wee bit of the rascal about him, which I don’t mind. It makes him the player he is.”
Lennon has so far added just former Norwich striker Grant Holt to his ranks but will now focus his sights on securing a new goalkeeper ahead of next Thursday’s Europa League qualifier, which will likely see Brondby arrive in Edinburgh as opponents.
Last season’s Scottish Cup-winning stopper Conrad Logan has yet to be offered fresh terms following the expiry of his short-term deal while Mark Oxley is weighing up a move to Southend.
That would leave Finnish youngster Otso Virtanen as the only senior stopper on Hibs’ books and Lennon is on the hunt for cover.
“I know there is interest from Southend in Mark and that will be his decision,” said the Northern Irishman. “But we’ve brought [former Raith Rovers understudy] Ross Laidlaw in on trial and we’re having a good look at him. He has impressed us so far.
“But we are still actively looking for a goalkeeper right now because we have to replace Conrad as well. Might he re-sign? Well you never say never but there are other options for us to look at.”
Brondby are 4-1 up from the opening leg of their first qualifying round duel with Icelandic side Valur and Lennon knows his troops will be up against it if the Danes finish off the job.
Hibs only returned to pre-season training at the end of last week and have just two warm-up games, against Berwick and Motherwell, before being plunged into European action.
“We’re not going into the game with huge expectations but we do want to compete,” he said. “They are a good side. For a long time they have been one of the best Scandinavian clubs on the European scene. They are very strong domestically and have very good European pedigree.
“It was always going to be a difficult fixture to negotiate because basically all we have is two pre-season games then we are straight into it.
“The home tie is the first game and you never know what can happen. We need to take some kind of advantage with us over to Denmark.
“It’s been the year of the underdog when you look at Leicester winning the Premier League down south and the likes of Albania, Northern Ireland, Iceland and Wales having had a fantastic time at the Euros.
“It shows it can be done. However, they have had weeks of preparation. We’ve had 10 days tops.”
Meanwhile, central defender Jordon Forster, who spent time on loan at Plymouth Argyle last season, has signed a new two-year deal with Hibernian.