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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.