The team is also not saying if the captain will need surgery.
According to a report in The Toronto Star, Sundin could potentially need retina surgery to correct his "cloudy" vision after getting hit in the face by a flying puck two weeks ago.
"We are not dealing with an exact science in terms of healing and recovery," Leafs GM John Ferguson told the newspaper. "We have never stated anything about a time line (for Sundin's return). … There will be further tests and we will continue to monitor him very closely."
Ferguson also told The Star that he could not accurately comment on the potential surgery, or why Sundin's vision remains impaired, because of the slow healing process.
According to the report, Sundin's eye sustained a certain level of damage and has residual blood that prevents doctors from making a decision on surgery and his return.