Southampton reportedly lodged a £10million offer for the Kenyan midfielder but Boyd suggests they should hold off and wait for a real bid to find its way into the Parkhead inbox.
"I don't think £10m would be enough for Victor Wanyama. I'd certainly be hoping for a lot more than that," said Boyd.
"Victor and Gary Hooper are the two I'd like to see stay, but Gary's different in that he's coming into the last year of his contract and there's a risk he'll leave for nothing at the end of that.
"Wanyama still has two years left on his contract. Neil Lennon said he wanted £25m for him and I'd go along with that. Why not? If the bidding is to start at £10m then there's a lot of room for it to go up."