New United boss Louis van Gaal knows the 24-year-old well, having only just stood down as Netherlands manager.
And, although Strootman missed the recent World Cup due to injury, reports in Italy have claimed that the Premier League club are still interested and have put in a bid of at least £30million.
But Garcia said: “Strootman is a Roma player, he will be a Roma player this year. There is no doubt about that.
"Only he can say whether he wants to stay but it was never an issue for him to go to another club. There is no question of it."
United play Roma in a Denver friendly on Saturday but Strootman will not feature as he continues to recover from the cruciate knee ligament injury he suffered in March.
“Strootman is following a normal recovery programme,” said Garcia. “He has stayed in Boston (where Roma played earlier in the week) to work with our physios and he will start running any time soon."
Former Chelsea man Ashley Cole is likely to feature for Roma against United at the Sports Authority Field and Garcia is pleased with how the former England defender is adapting to life with his new club.
"He is keen to learn the language," said the Roma boss.
"He wants to communicate with his team-mates on the pitch in Italian, and I like and appreciate his attitude."