The Edinburgh side have made a major show of intent by luring the former Celtic manager to the capital.
But Alan Stubbs’ replacement knows his job will be made significantly harder if he cannot keep hold of his highly-rated youngsters.
Both midfielder McGinn and striker Cummings played key roles for Hibs as they helped end the club’s 114-year wait for Scottish Cup glory last month but the thought of another season in the Ladbrokes Championship following their failed promotion bid could attract suitors.
But Lennon, 44, hopes to sell them a vision that ultimately ends with Hibs returning the upper echelons of the Scottish game.
He said: “John and Jason are excellent players who have just had terrific seasons.
“They are vital to what I want to do so I’d like to sit down and speak to the both of them.
“I’m hoping they will see things my way and want to stay for a while.”
But he admitted it is unlikely Anthony Stokes will be checking in for a second Easter Road stint, despite Celtic releasing the striker on Wednesday.
Lennon signed the Irishman - who spent the second half of last season on loan with Hibs, scoring two goals in their cup final triumph over Rangers - during his spell as Celtic boss back in 2010 but is doubtful he will be linking up with the 27-year-old again.
“If I could get him here it would be fantastic but I think that may be beyond us in terms of finances,” he said.
However, Lennon believes he will get the resources he needs to ensure it is third time luck for Hibs’ promotion aims.
“I know the budget is strong,” he said. “That was never an issue in coming here though. It’s the challenge that interests me more.
“I need to now sit down with the players I want to keep. There are players making waves to try and go but I don’t want that to happen.”