The 19-year old midfielder, currently on loan with Blackpool, was born in England but has a Scottish grandfather and Levein is hoping to lure him into the Tartan Army.
"We've been in touch and we are hopeful," he said.
"As usual, we will continue to try and unearth as many players as possible who are eligible to play for Scotland.
"We want as many good players as possible to be able to play for us."
Shelvey, who has been capped by England at youth level, has been on fire for the Seasiders with four goals in seven appearances since arriving on loan in late September.