Wanyama told the Daily Mail: "My manager Neil Lennon told me of Southampton's offer but while the bid was okay for Celtic, the terms were not right for myself and my agent. I am open to what offers are made but I am relaxed and it's important Celtic are happy too.
"My agent and I have been together a very long time and we are like family. We have a very good relationship. He has helped me since I was a young man and there is a lot of trust between us. I know he will help me make the right decision over the next few weeks.
"This is a very important move for me if it happens. I've had two very important seasons at Celtic and I've had the opportunity to play in some very big games and with some talented players. My dream, like any young footballer, is to play in the Premier League and maybe that is the next step for me."