Greer told BBC Sussex: "If it was offered to me I'd be delighted. I was captain at Swindon and had a fantastic year there last year.
"I'm just looking forward to getting started and meeting the other players."
He added: "There's a good squad of players so I definitely feel the club can be challenging up there."
Albion boss Gus Poyet is still waiting to decide who will step into the void filled by departed captain Andrew Crofts, who has joined Championship side Norwich.
"We've been talking about it because it's not an easy decision. It's a very important one," the Uruguayan said.
"Sometimes it's a very easy one because you have the right character or the right person to do it.
"We're going to wait until we've got the full squad."
Source: BBC Sport
Source: BBC Sport