He said they could be recalled in the wake of VW`s emissions cheating.
The paper reported that about €1.8bn (£1.3bn) of those loans are still outstanding.
Mr Hoyer is quoted as saying that the EIB had granted loans worth around €4.6bn to Volkswagen since 1990.
"The EIB could have taken a hit [from the emissions scandal] because we have to fulfil certain climate targets with our loans," the Sueddeutsche Zeitung quoted Mr Hoyer as saying.
Mr Hoyer was attending the International Monetary Fund`s meeting in Lima, Peru.
He added that the EIB would conduct "very thorough investigations" into what VW used the funds for.
Mr Hoyer told reporters that if he found that the loans were used for purposes other than intended, the EU bank would have to "ask ourselves whether we have to demand loans back".
He also said he was "very disappointed" by Volkswagen, adding the EIB`s relationship with the carmaker would be damaged by the scandal.
Volkswagen admitted that about 11 million of its vehicles had been fitted with a "defeat device" - a piece of software that duped tests into showing that VW engines emitted fewer emissions than they really did.
Mr Hoyer`s comments come days after VW`s US chief Michael Horn faced a Congress panel to answer questions about the scandal, which has prompted several countries to launch their own investigations into the carmaker.
On Monday, VW`s UK managing director Paul Willis is due to appear before members of parliament at an informal hearing.
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