Wigan Athletic have been linked with the 34 year-old striker and former Manchester United midfielder Greening: "It will be massive to keep Kevin Phillips. He has scored so many goals for us this year - but it is not just that which is important.
"It is his aura around the place. He is one of the jokers of the place, one of the lads who brings the team spirit together.
"Hopefully the chairman (Jeremy Peace) will sit down with him and sort out a new deal sooner rather than later and Kevin can have a good summer and prepare for next year."
Greening added: "You only have to look at Teddy Sheringham and the impact he has made. He played at West Ham in the Premier League until he was 38-39.
"He had a great soccer brain and Kevin has the know-how up top which will definitely help us in the Premier League.
"He is one of those players like Teddy who drops in and holds the ball up well for us and you need that in the top division and I am sure the gaffer will be desperate to keep him."