McNamara is currently short of defensive options after Gavin Gunning suffered a knee injury which it is feared will rule him out for the rest of the season.
Former Hammarby player Tornstrand has linked up with the club for a training stint and McNamara has challenged the 23-year-old to impress.
"We'll have a wee look at Marcus. I haven't seen all that much of him and the difficult thing is trying to get a game to have a look at him in," the Dundee United boss said in the Daily Record.
"But I know he has played for Sweden's Under 21s.
"The transfer window is shut just now so there's not a lot we can do but we'll have a look.
"With Gavin Gunning getting injured we are a bit short at the back to say the least."