The trio all played the full 90 minutes during a 2-1 win over Chelsea in the EFL Cup on Wednesday, with Rashford sealing the game with a brace.
Solskjaer confirmed after the game that all three had suffered knocks but stressed that he expected them to return in time for Bournemouth.
However, according to ESPN‘s Rob Dawson, the trio have not recovered as quickly as Solskjaer would like.
Maguire, Rashford and Lindelof are doubts for United's trip to Bournemouth tomorrow. Will have a light session today to see if they can play. Shaw, Matic, Tuanzebe and Pogba out until after the international break.
— Rob Dawson (@RobDawsonESPN) November 1, 2019
Having finished the game late on Wednesday night, followed immediately by travel to Manchester and then a plane down to the south coast, the turnaround for these players is not a very big one – especially after what was an intense affair at Stamford Bridge.
The injuries leave United without their first-choice centre-back pairing for the first time in the Premier League this season, laying the platform for Marcos Rojo and Phil Jones to start the game, while Juan Mata could come into the side as Daniel James moves over to the left to replace Rashford.