Jon Miquel Toral Harper, who turned 16 on February 5, has been hailed in Spain as the new Cesc Fabregas, the Arsenal captain who left Barca's youth school for London at the same age in September 2003.
Rosell said in an interview with Catalan television late yesterday that club officials had told Arsenal counterparts before last week's Champions League last-16 first leg they were unhappy with the way the deal was conducted.
Spanish media have reported it was brokered by Barca coach Pep Guardiola's brother, who is a football agent.
"It's very important to keep this group of young lads together with a grounding in our way of playing football," Rosell said.
"We don't like it when other clubs come with offers of money just before the (player's) 16th birthday," he added. "It's legal but a little immoral."
Rosell was also asked whether Barca will make another effort to bring Fabregas back to the club during the summer transfer window.
The 23-year-old Spain international is seen as an ideal replacement for playmaker Xavi, who turned 31 in January.
"Barca must have the best possible team and we have to fulfil the requests from the technical staff without forgetting the economic situation and that Barca has to pay salaries and costs," Rosell said.
"If Cesc comes, because the technical staff want him and he wants to, the club members would accept it."
Meanwhile, David Villa, the Barca striker, is convinced his side will beat Arsenal to progress to the quarter-finals of the Champions League next month, despite last week's 2-1 defeat in north London.
Villa gave a dominant Barca side the lead in the first leg at the Emirates last Wednesday, only to see Arsenal hit back to claim what had looked an improbable victory through second-half goals from Robin van Persie and Andrey Arshavin.
"I think that if we do things like we did in London, we will be on the right track," he said.
"We will go through to the next round, I'm sure, because we were far superior in everything except for the result (at the Emirates)."
Villa and his teammates missed a host of clear-cut chances in London, though, and the Spain forward knows passage to the quarter-finals will depend on their shooting accuracy in the second-leg.
"We need to perform better in front of goal," he said. "If we do that we will go through."