A source close to the Ireland South MEP said he was speaking to TDs and senators and was happy with the support he was receiving across the Fianna Fail parliamentary party.
Mr Kelleher is a former Cork North-Central TD and junior minister who worked as a farmer before becoming a politician.
Reports have suggested that former Dublin football manager Jim Gavin could also be a possible Fianna Fail nominee.
Fianna Fail’s parliamentary party is expected to make a decision on the presidential election in the early autumn.
Earlier on Thursday, Independent candidate Catherine Connolly said political parties in Ireland which have not yet decided on whether to run a candidate for the presidency are “disrespecting” the constitution and the role.
Ms Connolly denied that she was using a visit to w