Scotland full-back Paterson, 22, is out of contract at the end of the season.
Should the defender leave Tynecastle in the summer, Hearts would be due a development fee of around £450,000.
Levein added at the club's annual general meeting that new head coach Ian Cathro would be provided funds for next month's transfer window.
However, Levein said the ultimate aim was to provide players for the first team from Hearts' academy.
Meanwhile, club owner and chairwoman Ann Budge announced plans to launch a debenture scheme in 2017 to try and bridge a £3m funding gap for the redevelopment of the main stand at Tynecastle.
Renovation works have already started and the ground's capacity will eventually increase to more than 20,000.
Budge says the club have no plans to go into debt to fund the £12m development.
She told around 400 shareholders that commitments from fans' group the Foundation of Hearts and club benefactors of £3m each will also help with the total cost, with £2.5m having already been spent on the preparation of the new stand.
And Budge told BBC Scotland: "I've had a number of supporters contact me already and say, 'can I have a lifetime membership?'
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"I don't want it to become a stand purely for the corporates and people who can spend hundreds of pounds to come to football. We've got to offer something for a full range of supporters and that's really what we're trying to do.
"I genuinely don't feel it's a risk as long as the supporters keep supporting us - that's the key factor.
"If for whatever reason that started to tail off, then we would have a problem but the comfort for me comes from knowing that we have already enough to build the stand, to get the seats open, to increase the capacity and then if we run into one or two cash-flow issues, we've got time.
"If we don't kit out or fit out all the space in six months, it doesn't really matter. We know we've got enough to do phase one."
Hearts would only be willing to sell Callum Paterson in January for a "seven-figure sum", according to director of football Craig Levein.