Berahino is settled at West Brom and it is understood Albion are confident that he will be given the contract he deserves by the board. His deal runs out at the end of the season and there is also an extra year's option in the club's favour.
But the threat of a possible bid from a more established Premier League club is a worry for Steve Clarke, who gave the Burundi-born forward his first league start against Arsenal last weekend, and wants negotiations to be concluded before the end of the year.
"He's under contract with West Brom until the end of next season, so we've got plenty of time to sort out Saido's future," said Clarke.
"He's a sensible boy. He understands that all the rewards and riches come with hard work and he has to just concentrate on his football and let other people worry about his contract situation and whatever.
"Saido has got a big future in the game and all he can do now is work hard and make sure he is still a top player in ten years' time."
Clarke has already suffered frustration in his bid to keep another home-grown Albion player this year, after Chelsea signed highly-rated midfielder Isaiah Brown in a deal that is set to go before a tribunal.