The Spanish midfielder is being linked with a move to the Reds from Bayern Munich.
But the club are stalling on his fee, as they could sign him on a free transfer next summer.
"To get to a Champions League final, win it the following season, and then to go again to win the Premier League title is a huge emotional drain on that group of Liverpool players for three years," Neville said on Sky Sports.
"To ask them to go again and achieve that same standard would be a superhuman effort.
"It wouldn't be ridiculous to suggest there will be a slight drop-off, if they don't somehow stimulate that squad by doing something to give them that lift again.
"Thiago would be the big one. He is world class and would give them a world-class presence in an area of the field where they don't have one."