McAteer believes his former club would be better served by rivalling Manchester United for the signature of Sancho this summer.
"Sancho will be a great acquisition," he told beIN SPORTS. "I think Liverpool should go out and buy him. "He can be a great player for Liverpool and I think we need to take pressure off the front three."
On the Reds' oft-discussed interest in Werner, he added: "It's whether he is the right fit.
"We know Jurgen doesn't just venture into the transfer market to buy a superstar just because someone is available or because he has got money in his pocket.
"He might want to go to United, which is the talk at the minute. Timo Werner might be the player we go for if we don't get Sancho."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!