Spurs announced that Conte would not be in the dugout for Sunday's clash with West Ham United. He returned from having had gallbladder surgery for last weekend's 4-1 drubbing by Leicester City but remained in Italy after Tuesday's 1-0 defeat by AC Milan in the first leg of their Champions League last 16 tie.
"Since he came back he felt that maybe he underestimated the procedure after the surgery," Stellini told a news conference on Friday.
"Then coming closer to the game the stress of it all, it created some problems and when he spoke to the doctor they said he needed to take it easy. He will be back soon but not as quickly as he would like.
"We have a call every day, maybe three times a day and every time he wants to come back. He repeats every day 'I want to come back Cristian, how was the training? We have to organise this tomorrow.'”
Stellini confirmed that there are no new injury concerns for fifth-placed Spurs, who are winless in their last three matches in all competitions, ahead of the visit of struggling West Ham.
The assistant said that it has been "strange" to receive such a warm response from Tottenham fans during the period in which he has taken over Conte's first team responsibilities.
"It's strange for me," the Italian added. "Not many people know the assistant. Who knows the assistant? This is a strange thing for me. I repeat that I'm not alone though, there are many people who work with me.
"(First team coach) Ryan Mason was important every time and will be this weekend. He is important for me and all the staff, (Constantino) Coratti, (Stefano) Bruno (fitness coaches) and (Marco) Savorani for the keepers.
"What we are learning now is that Antonio takes responsibility with great character. He asks the assistants but he takes the decisions.
"Now we have take responsibility together. We're more like a team. When Antonio is here, he will take decisions, he takes the responsibility and sometimes doesn't explain why."
