Berahino has impressed for West Brom recently and scored the winning goal against Manchester United last weekend.
The England Under 21 international’s current contract is set to expire at the end of the season.
“It is very important for Saido and for the club because he doesn’t need speculation starting,” McAuley told the Express & Star.
“He doesn’t want anything that will make him take his eye off the ball.
“I’m sure there is a lot of stuff going on behind the scenes to get that sorted, and the sooner it’s done the better.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.