The 20 old has shot to the top this season with impressive displays for club and country including a hat trick in the Capital One Cup and the winning goal away at Old Trafford.
The likes of Manchester United, Arsenal and Tottenham have been scouting the youngster in recent weeks and could prepare big money January bids that keeps the youngster from signing the new deal.
West Brom will be desperate for the striker to commit to the club, for financial safety if nothing else, and they are prepared to times his current salary by ten to do so.
“He has scored some goals for the under-21s against opposition that is not the strongest, it has to be said,” Clarke said.
“He has scored a Premier League goal for us and he is doing alright but at the moment I would like to see everyone back off and give him time to develop as a player.
“I will try and look after him, rest him at the right times and play him in the right games. I will try to keep his confidence high and not allow him to get carried away with his emotions or get over-confident or cocky. I will manage him as best I can.
“Saido’s contract is under discussion. Everyone is talking about it. Three weeks ago I said I was confident something would be sorted and I’m still confident something will be sorted.”