Bellamy has one year left on his current contract with the Merseyside outfit, and Rodgers insists after talking with the former Manchester City man that he wants his talent and enthusiasm at Anfield.
"I had a really positive chat with Craig on Monday," Rodgers told the Liverpool Echo.
"It was good to meet him and get his side of the Liverpool story. He's a big supporter of this club - he loves the club. He's a good guy. He has a real passion for Liverpool Football Club and that's the type of people I want here.
"I like his intensity, his work-rate and his passion so I would love him to be here."
And the Reds' boss believes it would take a spectacular offer from another club to force a parting of the ways between Bellamy and Liverpool.
"He's a player. It would take a really special and unique opportunity for Craig to walk out of Liverpool and for us to go our separate ways.
"If anything changes on that from a personal perspective then him and I will talk about that."
And despite Bellamy's inclusion in the Team GB squad for the forthcoming Olympic Games, Rodgers insisted he will keep in close contact with the Welshman.
"Craig is off now for the Olympics but we have promised to keep in touch," said Rodgers.
"He's obviously got a year left on his contract and going forward we will discuss more where he's at.
"This week was really just a formal introduction. Of those who aren't back, I've spoken to a lot of players over the phone and met one or two. In particular the senior players I'm keen to chat to and meet with.
"Craig and I had a really good chat about football in general. He has probably seen closer more than anyone at the club how I worked down at Swansea.
"He was very complimentary about that work and thinks I'll be a perfect fit for here."