Bramall is understood to have been on trial at Hillsborough and played in Wednesday's second string defeat to Nottingham Forest last week, but failed to make any real impression.
The 20-year-old's Everton contract expires this summer and it would seem that he's free to leave Goodison Park, where has found himself on the periphery of the Premier League club's own U23 side.
But his chances of following his former Toffees teammate, Jordan Thorniley, to Sheffield Wednesday now look slim.
It is three years since Thorniley, who has since appeared 33 times for the Owls' first team, moved to Hillsborough on trial from Everton and later earned a permanent contract.
Bramall was born in Sheffield and joined the Toffees from Chesterfield's youth system in 2015.
Sheffield Wednesday's U23s end their campaign against Queens Park Rangers next Monday and it will be interesting to see whether or not Bramall is given another chance to impress the Owls.
Have something to tell us about this article?