The franchise is being established to participate in an expanded Super rugby competition from 2011 onwards and will play their first game against Ian McGeechan's tourists on June 16, under the name of the Coastal XV.
Meyer returned to South Africa earlier this season having being released by Leicester on compassionate grounds after his wife's parents were taken ill.
Stormers coach Rassie Erasmus has also been linked to the job in recent weeks but Meyer's more extensive coaching record carries appears to make him the favourite for the new position.
If Meyer does lead the Coastal XV against the Lions he could be reunited with one of his former players, Harry Ellis. The England scrum-half is the only Tiger in the Lions' 37-man party and played under Meyer for the opening months of the season.