Rosell has just won the presidential elections at Camp Nou, succeeding Joan Laporta.
Laporta first instigated Barca's move for Fabregas earlier this summer and Rosell will continue their pursuit.
"We are not under any sort of pressure at the moment," said Rosell.
"We have the whole summer to sort this deal out.
"I am convinced that Cesc will be our player by the start of next season. I know what happens in football and I will not be surprised to see stories of other clubs chasing him.
"But we are very calm because the key person in all of this is Cesc himself.
"The only way he will leave Arsenal is if he is joining Barcelona because of his roots."
Reports on Thursday suggest Barca are ready to offer Arsenal a final 'take-it-or-leave-it' £40million for Fabregas.