Shaw was the only United player to start every Premier League game last season, becoming just the fifth outfield player to have started all 38 top flight games for the club during a campaign.
The 31-year-old had an incredible season as he brushed off injuries and was there for the Red Devils when they needed him, week in, week out.
The England star has entered the final year of his deal with United, who have the option for a one-year extension so they don't lose him for free next season.
Speaking to Sports Mole on behalf of NetBet Sport, Pallister believes United need a backup for the veteran who despite his fine season last year, is still prone to injuries.
"Neco Williams is a young lad who has shown promise," Pallister said. "I thought Luke Shaw had a really good season, but there is always going to be some doubt because of his injury history. He still has something to give so I would still see Williams as a backup for him.
"United are back in Europe and you can’t expect Shaw to play twice a week, every week. Williams will offer strength in depth, and he’s an exciting player, so I think it’s a good move."
Williams has close ties with Liverpool, having come through their academy, which may add complications to his United move as Liverpool academy players rarely get a move to the Red Devils.
The bad news for United is that Williams is reportedly discussing improved terms at the City Ground after an impressive 2025-26 season, when he scored twice and contributed four assists across all competitions.