Vilanova, 44, needed a second round of surgery in December following an operation to remove a tumour from his saliva glands in November 2011 and his assistant Jordi Roura has taken charge until he is well enough to return.
Although they are still 11 points clear at the top of La Liga, Barca have stuttered in recent weeks - losing 2-0 at AC Milan in last month's Champions League last 16, first leg and going down twice to arch rivals Real Madrid last week.
Rosell said the coach was midway through a course of chemo- and radiotherapy and when he visited him in New York last week was "in very good spirits" and "very involved in the day to day activities of the club".
"There is no doubt that a group gets weaker when they lose their leader," Rosell told a news conference following a routine meeting of the Catalan club's board of directors.
"Sports psychologists say, and I suppose there is a scientific explanation to it, that after 30 days the group's shape weakens," he added.
"We have been without our leader for a long time now and it is normal to see this happening.
"He is longing to come back, hoping for the process to finish, which is due at the end of March.
"The other day he told me he was happy because he could start the countdown as he is over half of the process and he has less than 50 percent of it left.
"That is very good for his state of mind. He wants to come back and we want him back."
Some media reports in Spain have suggested Barca were considering bringing in a temporary replacement coach but an emotional Rosell categorically ruled it out.
"The absolute priority of the club this season is for Tito Vilanova to get his health back and everything else is of secondary importance," he said.
"I want to thank Roura for his work, he is a hero. We must thank him enormously for what he is doing because it was not his responsibility.
"Also the players who are suffering this burden and are still top of the league.
"Nothing will change here until Tito returns even if it costs us all our titles this season.
"I would consider it a successful season if Tito was back to full health by the end of it."
Barca have a La Liga game at home to bottom side Deportivo La Coruna on Saturday before they host Milan at the Nou Camp on March 12.
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