Thompson was on the books of United from 2011 until 2015, but he failed to make a breakthrough into the first team.
The 19-year-old was released by the Premier League giants in the summer of 2015, and he subsequently joined Scottish side Rangers.
The talented teenage midfielder has yet to make a major impact at the Gers and had a loan spell at Airdrieonians this season.
Thompson played with 18-year-old forward Rashford at United’s youth teams, and he has revealed how much he rates him.
“While he [Marcus] is younger than me I can still look up to him playing in the Premier League and I just want to take my chance if I get it next year,” the Rangers youngster told the club’s official website.
“It’s brilliant seeing those boys do well, I love seeing it, my other mate Joe Riley is at United too and he made his debut in the Europa League.”
“I played with him at United and we’re friends, we still speak now,” added Thompson. “Marco was always brilliant on the ball and he just had to get better off it and improve his work rate, which he has learnt from playing with the first-team. He has taken the game by the scruff of its neck whenever he has played.”
Rashford has scored four goals and created six chances in 10 Premier League appearances for United this season.
The 18-year-old forward has a pass accuracy of 78% and a shot accuracy of 88%, and has won three headers, seven dribbles and six tackles.
The United youngster has also been named in the provisional England squad for the Euro 2016 finals in the summer.