An Irish Examiner/Prime Time poll revealed that Fianna Fáil's second MEP in the constituency, Gerard Collins, could lose to Independent Kathy Sinnott.
Mr Collins secured 15% of the first preferences in the poll while Mr Crowley got 30% enough to elect him on the first count.
The poll prompted Fianna Fáil director of elections John O'Donoghue to appeal to Mr Crowley to stop invading his running mate's designated territory and canvass only his own area.
"I cannot go around with a flash lamp and a stick after Brian Crowley I would just appeal to him to honour the pledge he made on the day he got his nomination to obey his director of elections' rules," Mr O'Donoghue said.
He added he was not going to start disciplinary procedures in the middle of an election campaign.
"I would just appeal to Brian Crowley as a matter of honour to please, please, help the party and stop his continuous invasion of Gerry Collins's territory."
The poll saw Fianna Fáil get a combined 45% of the first preferences enough, Mr O'Donoghue said, to secure their current two seats with a proper vote management strategy. This includes a clear divide of the South constituency that would give Mr Collins the right to canvass exclusively in Kerry, Limerick, Tipperary North, Waterford county and the Mallow area.
Mr Crowley has the right to canvass in Cork City and County except Mallow Tipperary South and Waterford City.
But Mr Crowley yesterday insisted that he was not going to change his campaign strategy.
"I was not consulted about the constituency divide and disagree with it. I believe the voters in the South constituency should have a chance to question every candidate, not just the ones chosen by the party," Mr Crowley said.
He added that he was not concerned that this would lose Fianna Fáil its second seat in the South. Mr Crowley said: "My campaign strategy has not changed it is the same strategy that succeeded in delivering two seats for Fianna Fáil in the past."
Mr Collins said he has respected the decision to divide the constituency. "The only way for Fianna Fáil to win the two seats is to abide by the strategy," he said.