The three players have featured in all four of their respective club's opening Premier League fixtures so far this season.
It comes after Jack Grealish and Trent Alexander-Arnold both pulled out of the side with minor injuries earlier this week.
However, the Evening Standard claims that the issues are not serious, and the players are just being watched closely, and instead of training with the whole squad, the three players had less taxing solo sessions in order to manage their fitness.
Wilson has only been a sub in Newcastle United's first four games of the season, but he does have a lengthy backlog of injury concerns across his career.
Saka and Colwill meanwhile, have played almost every minute of the season so far, with the Chelsea defender also playing an hour in their EFL Cup tie with AFC Wimbledon last week.
Colwill is uncapped at senior level, and Chelsea sent the 20-year-old for a scan prior to meeting up with the England camp to ensure he was fully fit.
However, as a precaution, he trained in private, meaning he could be being protected in order to potentially make his international bow this week.
In their absence, Alfie Devine and Bashir Humphreys, two current England youth internationals, were drafted in to train, along with recent Newcastle recruit Lewis Hall.
England face Ukraine on Saturday in neutral Poland in the Three Lions' only Euro 2024 qualifier during the upcoming international break.
After that, England will face Scotland at Hampden Park in a friendly commemorating the 150th anniversary of their clash which was the first-ever international match.
England will also miss the next international matchday in October due to the uneven number of teams in Group C, but a win over Ukraine will guarantee they will stay top until they next play.
Regardless of the result in Italy's encounter with North Macedonia, an England win on Saturday will move them nine points clear at the top of the group, where two sides will progress automatically to next summer's finals.
England's three group rivals will all then face each other before Gareth Southgate's men are back in action against Italy on October 17.