The midfielder has hinted that a move to the Premier League is an option at the end of the season, but his coach believes his future lies in Munich
Guardiola is keen to keep the midfielder despite the interest of the Red Devils, and suggests that Kroos' "huge personality" has been integral to his debut season in charge of Die Roten.
"I said to him you have time to become an even better player," Guardiola told reporters. "I hope he maintains this level of form — and for the next few seasons at this club. Toni is a young player, a great talent. He has time to improve, to gain better his skills. I spoke with him and said you have time to become a better player.
"He was very important in my first year here, in the first part of the season when [Mario] Gotze , [Javi] Martinez and Thiago [Alcantara] were injured, so we had few midfielders. Kroos, with his huge personality, was very important."
Kroos' impressive performance for Bayern in the first leg of its Champions League last 16 tie against Arsenal at the Emirates attracted further transfer speculation, while Die Roten host the Gunners on Tuesday with Arsene Wenger's men looking to overturn a 2-0 deficit.