The 20-year-old has been outstanding this season, steering third-placed Leverkusen within three points of leaders Bayern Munich while also winning his first international cap two weeks ago.
Kroos, banned for last week's win against Hamburg SV, has been the driving force in midfield, scoring nine goals and playing a part in several more as Leverkusen chase an elusive Bundesliga title.
"Toni would like to stay with us," Leverkusen sports director Rudi Voller told reporters.
"Whether it is in the form of a loan or whether we buy him that is a minor issue. I will do everything possible so he stays.
"Toni will become even better if he stays here for another year," added the former Germany coach.
"We showed we are back on track with our win against Hamburg," said striker Eren Derdiyok, who has netted 12 times this season.
"It was good to see we managed to cover well for the absence of Kroos but now we have the tough matches (against Dortmund, Schalke 04 and Bayern) coming up."
Coach Jurgen Klopp's Dortmund have climbed to fourth, scoring seven goals in the last two matches.
