Shaw was named in Tuchel’s 55-man provisional squad and there had been a clamour for his inclusion.
But, with Newcastle’s Dan Burn and Manchester City’s Nico O’Reilly in line to be called up, Shaw is expected to miss out.
Chelsea defender Levi Colwill and AC Milan defender Fikayo Tomori are understood to be out, though Arsenal winger Noni Madueke is thought to have made the cut.
He joins his Premier League-winning team-mates Bukayo Saka, Declan Rice and Eberechi Eze, who is set to be rewarded for his excellent form with a place in the 26.
Tottenham defender Djed Spence has also made Tuchel’s squad, meaning there is no place for Real Madrid’s Trent Alexander-Arnold, Arsenal’s Myles Lewis-Skelly or Everton’s James Garner.
Spence, 25, suffered a broken jaw in Tottenham’s 2-1 defeat by Chelsea on Tuesday but is expected to wear a protective mask if he plays against Everton in the Premier League on Sunday.
The omissions of Maguire, Tomori and Colwill mean Manchester City defender John Stones is very likely to be included, despite his injury-disrupted campaign.
Tuchel views Stones as a key player but has been concerned about the departing Manchester City man’s fitness.
Crystal Palace midfielder Adam Wharton is another poised to miss out, but Manchester United midfielder Kobbie Mainoo is set to keep his place in the squad after earning a recall for the previous friendlies.
There is an expectation that Brentford midfielder Jordan Henderson, who has been a mainstay under Tuchel, will keep his place.
The World Cup, which takes place across the US, Mexico and Canada, starts on 11 June.