Drogba last week signed a two-and-a-half year contract with the Chinese club but broadcaster TV3 claimed the striker has a clause in his contract with Shanghai that allows him to talk to Barcelona and that the striker was ready to invoke it to move to La Liga.
It was reported Drogba was travelling to Catalunya for talks, but Rosell said: "I don't know anything of Drogba. If he's here he's come on holiday or for something personal. It's nothing to do with Barcelona."
Drogba's representatives also tweeted: "Drogba to Barca story complete nonsense. As we told you he joins Shanghai in July."
However, Barcelona have set aside an average of 40 million euros per year to spend on players and are in talks with Valencia to buy Spain full-back Jordi Alba.
"I am not happy these negotiations (for Alba) have leaked out but they have," Rosell told a news conference as part of his annual review of the season.
Alba, who has turned in excellent performances at left-back for semi-finalists Spain at Euro 2012, started out in Barca's youth ranks and could return in place of France international Eric Abidal who is recovering from a liver transplant.
Spanish media have reported Valencia want 15 million euros for the player, who turned 23 in March.
Rosell added preliminary financial results for the 2011-12 season suggested Barca would make a profit of 40m, almost twice as much as the projected 21m.
The cash will be used to pay debts which stand at a net 340m.
Plans to refurbish the club's giant Camp Nou arena have been put on hold as debt reduction takes priority, Rosell said.