The 18-year-old joined Pompey in 2011 from Lewes after he began his career with Farnborough Town.
This season has seen him make rapid progress and, after scoring eight goals in just 11 games for Whitehawk while on loan, he was recalled to Fratton Park.
He has since become a first-team member under Guy Whittingham and has bagged two goals in seven appearances from midfield.
Wallace was attracting interest from Premier League clubs while at Whitehawk and now Sky Sports understands Pompey rejected two bids from Football League clubs - believed to be Brighton and Port Vale - in January.
Portsmouth revealed to Sky Sports that they had shunned interest in Wallace last month.
"There was some interest in Jed before the transfer window closed but we won't reveal who that was from," a spokesman confirmed.