Gerrard has already been named Rangers boss, while Lampard is on the brink of the Derby job, according to reports.
Now BT Sport want outspoken former Man United star Keane, 46, to fill the void left by his fellow Premier League alumni.
Keane currently serves as Martin O'Neill's No2 at the Republic of Ireland – and will be one of ITV's top pundits during this summer's World Cup.
Now, according to Sportsmail, BT Sport are set to offer the Irishman a lucrative contract to be part of their Premier League and Champions League coverage in 2018-19.
The BT Sport panel joked about their current threadbare roster of pundits following the Champions League final on Saturday.
Addressing Gerrard, Lampard and Rio Ferdinand, host Gary Lineker quipped: "What about you Frank, are you here to stay?
"We’ve lost Steven already, he is off to Rangers. Now lots of rumours about Derby.
KEANE TO HELP Man United urged by Roy Keane to sign ‘influential’ players this summer that help Paul Pogba
"Steven, wish you well. Whatever happens Frank, wish you well. Rio, thanks very much as ever."
Ferdinand joked back, saying, "I will be here", with Lineker responding, "Good, glad someone will be."
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