The young Scottish striker played in Gillingham's 2-1 friendly defeat to Notts County on Saturday.
Brighton given Gills trial
Gills boss Neale Cooper said: "I will be making a decision on Tom in the next couple of days and hope to have a few more triallists in next week so that we can have a look at them.
"There is no way I am going to just sign people just for the sake of it. We need another four or five players but I want to make sure those we do sign are the right ones.
"We are working within a budget and if I just jump right in and sign players willy-nilly, that would be a disaster."
The player, who can also perform on the flanks, returned to Rangers before Christmas after failing to make a real impression on loan at Glanford Park last season.
The Irvine-born player made six appearances for United, and featured just once for the Gers - that came in 2002.