Shilton, England's record cap holder with 125 appearances for his country, believes the Anfield talisman should get the job on a full-time basis.
He told talkSPORT: "I don't think it would be a bad move. I've been impressed with Steven in the recent matches. He speaks well, he's calm, he's got a bit of authority.
"He seems to be responding to it so it's hard to look and think 'who else would do a better job'?
"I've always been a fan of John Terry. He's a natural leader but you can lead in different ways. The great Bobby Moore, my first England captain, he wasn't a shouter who charged around the place. He led a bit like Steven Gerrard, nice and calm and collected.
The Spanish Liga outfit are chasing Reds midfielder Lucas Leiva and AS says they're also keen on teammate Ryan Babel.