A man capped on 56 occasions by England moved to Villa Park over the summer as a free agent after reaching the end of his contract at West Ham United.
Cole endured a difficult second spell at Upton Park, coming off the back of a forgettable three years on the books at Liverpool.
He is, however, far from a spent force and Villa are delighted to have picked up a player of his calibre for a minimal outlay.
Lambert said in the Birmingham Mail: “He is desperate to play and he’s got a right good chance.
“It is exciting because he has got so much to offer. He’s only 32 and some guys don’t even hit their prime until that age.
“I think he has still got the hunger to go and do as much as he can. And that’s from a guy who has won everything in the game.”
Lambert has also praised Cole for putting football above money, with the experienced playmaker revealing that he could have ‘earned a fortune lying on a beach’ had he decided to turn his back on the Premier League.
The Scot added: “When I spoke to him on the phone, he was desperate to do it.
“I knew it wasn’t a money thing right away. He’s not on a major amount of money or anything like that whatsoever.
“He wanted to play football. I think he knew he was coming to a right good football club with the opportunity to kick on again.
“I knew right away he wanted to play and that he was a proper guy.”