The 20-year-old arrived at Cantley Park last Tuesday after leaving the Scottish giants earlier this summer and featured in the friendlies against Spennymoor and Huddersfield.
Maxwell previously spent time on loan at Queen of the South and Ayr United in the Scottish Championship and turned down a new contract at Ibrox, meaning Rangers will be due compensation should he sign for Rovers.
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Gary McSheffrey delivered this verdict following Doncaster Rovers' late show at AFC Wimbledon
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McSheffrey said: “He looks quite comfortable, he understands the game.
"He's not had a big pre-season, he’s done a lot of individual training. So to come in and play 70 minutes then 66 minutes, I think he's done alright.
"I think he’s the type that will probably only get better.”
Despite his age Maxwell has already clocked up 75 appearances in professional football and represented the Gers in the UEFA Youth League, which pits the youth teams of Europe’s top clubs against each other.
A former winger converted to a wing-back, he also won four caps for Scotland at under-19 level between 2019 and 2020.
McSheffrey added: “He’s had a good start.
“As he gets fitter he looks a comfortable left-back to me. He’s one we’ll monitor and talk to over the week.”
Doncaster need a new left-back after releasing Cameron John and Branden Horton following last season’s relegation to League Two.
New signing Adam Long is left-footed but predominantly a centre-half.
Tommy Rowe is another left-footer who has previously played at left-back, although he has been deployed in midfield throughout pre-season.
Rovers host Rotherham United in their latest pre-season friendly tonight (7pm kick-off).