The Mayo footballer, who left the county panel days before their Connacht final earlier this month, is understood to be considering the invitation.
The 30-year-old was contacted by the Irish Olympic Handball Association (IOHA) shortly after he left James Horan’s camp prior to the Sligo game.
IOHA general manager Lúcás Ó Ceallacháin wouldn’t confirm whether they had been in touch with Mortimer. However, he admitted they would be interested in the Shrule man becoming a part of their preparations ahead of a trip to Estonia at Halloween.
“What we actually launched this week is a talent transfer programme where we hope to attract athletes from other sports,” said Ó Ceallacháin.
“Conor plays Gaelic football so he’d be a guy we would be interested in, but there are plenty of athletes from rugby to Gaelic games to basketball that could make the crossover.
“The programme is slightly unusual in that we are reserving two spots in our European Championship squad from these crossover sports. So of the 16 places in the squad there are two up for grabs and basically it’ll be a straight shoot-out for those spots between the athletes from other sports.’’
Mortimer’s availability is likely to depend on Parnells’ involvement in the Dublin SFC. Currently ranked 40th out of 50 countries in Europe, Ireland play their opening qualification game for the 2014 European Championships next October when they face Estonia.
They then face Belgium (twice) and Estonia again here next spring and summer.
The Cork hurlers’ current trainer David Matthews is their fitness coach while former Ireland rugby international Stephen McIvor acts as sports psychologist.
Despite leaving the panel after becoming disenchanted with a lack of starting opportunities, Mortimer has not closed the door on returning to the Mayo panel in the future.
However, speaking to RTÉ Radio One yesterday, team captain Andy Moran doubts Horan will make any attempt to convince the 2006 All-Star to return to Mayo colours this year. Moran said: “I think it was Conor’s decision more than James’ decision but to bring him back I don’t think that’s probably going to happen this year now.”