Leno arrived at the Emirates last summer but had to wait to prove himself to boss Unai Emery.
When Cech injured his hamstring against Watford in September, the German was ready to step up.
He played every remaining Premier League game, earning plaudits for his displays behind a defence that lacked solidity.
But Cech became Emery’s designated cup ‘keeper, playing in the FA Cup and Europa League campaigns.
The ex-Chelsea star was selected to face his former club in the Europa League final, causing Leno to express his displeasure.
According to the Evening Standard, the former Bayer Leverkusen stopper is now out to make himself No.1 in all competitions.
Arsenal have not entirely ruled out signing a new goalkeeper this summer after Cech’s decision to retire from the game.
But with just £40m available to spend, other areas of the team are considered a much greater priority to strengthen.
The Gunners are set to promote Emiliano Martinez to be Leno’s backup.
Martinez, 26, has been at Arsenal since 2011 but has made just six Premier League appearances in that time.
Meanwhile, Emery has been warned that selling striker Pierre-Emerick Aubameyang to Manchester United would spell disaster.
Former Arsenal star Ray Parlour thinks the touted transfer makes no sense, even if the north Londoners could raise upwards of £80m.
“It would be madness to let him [Aubameyang] go, but players have got all the power these days,” he told talkSPORT.
“Aubameyang and Lacazette have been absolutely brilliant this season.
“It looks like they’ve got a really good relationship up front, you can see how they celebrate goals.
“I’d be amazed by that [if he signed for United], I really would. That would shock me.”