The hospital confirmed that the allegations of incidents, which date back to the 1970s, were made after recent public allegations that the late presenter had sexually abused teenage girls, BBC News reports.
Trust spokesman Andrew Bannister said: "Two individuals have contacted the hospital to share their concerns about things that happened with Jimmy Savile in the '70s but these contacts have only come to light in the last few days since the upsurge of publicity.
"Clearly we will be liaising closely with the police because we also want to know what, if any, evidence they might have about any wrong behaviour in Leeds."
He added: "We did know him over a long period of time and there was nothing in his behaviour that would have given us cause for concern.
Copyright: flickr/BBC Pictures"We are shocked and upset at the nature of the allegations and the apparent conviction of the police that they need to be taken seriously. We wouldn't quarrel with that."
Savile volunteered at the Leeds hospital during the 1960s and 1970s and continued to do charity work for it until he died last year.
Leeds Teaching Hospitals NHS Trust said that no complaints had been received about Savile while he was working there.
The BBC has pledged to hold an independent inquiry into the allegations, while the police are following 120 lines of inquiry in Operation Yewtree, which is being run jointly with the NSPCC.