The 29-year-old has been at the Emirates since 2018 and managed to keep hold of his spot as No.1 despite competition from Emiliano Martinez towards the end of the 2019/20 campaign.
Martinez was sold to Aston Villa last summer, and Germany international Leno has continued between the sticks under Mikel Arteta, making 49 appearences across all competitions last season.
With Arsenal set to carry out a squad overhaul this summer, Leno is reportedly one of the senior players the Gunners are prepared to let go.
With Alex Runarsson their only other senior stopper, Sheffield United’s Aaron Ramsdale has also been linked with a move to the north London club.
And ex-Arsenal goalkeeper Seaman would welcome Ramsdale joining the north London club, if Leno is kept on as well.
‘I’d be disappointed if Leno leaves,’ Seaman told talkSPORT. ‘I’m asking myself: ‘Why’s he going?’
‘He’s been there a long time and been pretty consistent. Do I think Ramsdale would be good? Yeah, he’s a quality goalkeeper – he’s in the England frame – but I’d want both of them there.
‘I was very disappointed when [Emiliano] Martinez went as we need two quality goalkeepers at the club to test each other.
‘They let him go and there was no real pressure on him [Leno]. Getting other goalkeepers is good but if that’s at the price of a top international goalkeeper, I’m not too sure.’
Arsenal appear to be closing in on agreement to sign centre-back Ben White from Brighton for £50million, while they reportedly admire and are keeping tabs on Everton striker Dominic Calvert-Lewin.
Seaman believes both England internationals, who are currently on duty for the Three Lions at Euro 2020, would be good signings for the club.
‘People of that quality need to be coming to Arsenal,’ Seaman said of White. ‘I think we’re going down that route of players where they have young, promising with careers ahead of them.
‘The days of signing marquee players – that are right on it now – Arsenal will struggle with that as they’re not in Europe. The key players don’t just want to play in Europe, they want to play in the Champions League.
‘At the moment, Arsenal are nowhere near that and they need to restructure their transfer policy.
“Arsene Wenger used to pick out people and he’d sign them and we’d asked: ‘Who’s that?’
‘Then they turned out to be Thierry Henry!’
‘That would be a great signing,’ he added on Calvert-Lewin. “You want to be attracting those kind of players.
“Whether it happens, we will wait and see. With his proven goal-scoring record, why not?
‘There’s other positions we need. We also need a dominant centre-half with David Luiz going.’
For more stories like this, check our sport page