Vieira recently confirmed her departure from NBC's Today show in June, claiming that she wants to "enjoy life" and spend more time with husband Richard Cohen, who suffers from multiple sclerosis.
According to PopEater, Walters is keen to see Vieira return to The View, even if only on a part-time basis, as she believes the move would provide a ratings boost.
"Having Meredith back if only for a few days a week would make Barbara very, very happy. She never wanted her to leave in the first place," a source explained.
"Barbara adores Meredith and would welcome her back on The View in a second. Meredith returning home would be a great ratings boost and Barbara likes nothing better than ratings success even if it means asking one of the regular women to have a less active role."
Vieira previously confessed that she was unsure about departing Today and came to the decision at the last minute.