The 19-year-old arrived on a one-month loan last week thanks to Hargreaves' long-standing friendship with their Under-21 manager Warren Joyce and the Gulls boss hopes Rudge's addition is a sign of things to come.
"I'd like to get a closer link with Manchester United tied up, and this signing could be the start," he told the Herald Express.
"I've known Warren for many years, since we were both players. We are hoping to build bridges between the two clubs which, you never know, could lead to further signings in the future.
"He's (Rudge) with us now, and we'll hopefully give him some experience of football at this end of the game."