Gunners captain Fabregas is under contract until 2015 but has made no secret of his desire to return to the club he left as a 16-year-old in 2003.
Barca were unsuccessful with a £29million bid for the midfielder earlier this month but Laporta is trying to tie up a deal before Sandro Rossell officially takes over on July 1.
When, not if: Barcelona are confident they will sign midfielder Fabregas (right)
He said: 'It's difficult to sign Cesc before June 30 because Arsenal have a fixed position and it's difficult to change that position in a few days.
'If we cannot do that, then it will be in the hands of the incoming directors, and if they see fit, they will continue on this path.
'Arsenal will eventually give in, although I don't know when that will be. Therefore, everyone should wait and let the professionals take charge.'
Rosell said he would talk to Spain international Fabregas on a trip to South Africa, where he is on World Cup duty.
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