McCormack, who's scored 23 goals this season, tops the Seagulls' list of summer targets, a report claims.
The tabloid claims the Seagulls will have to pay £15 million to secure the striker, who signed a new long-term deal at Craven Cottage earlier this year.
Brighton are currently enjoying a 14-game unbeaten run which has propelled them to the precipice of the Championship's automatic promotion places, with only goal difference keeping them behind Burnley in third.
According to the Sun, Hughton is worried by his side's "lack of firepower" - despite having scored the most goals in the division alongside Burnley.
Israeli striker Tomer Hemed (16) is the only Seagulls player to hit double figures for league goals this season, a feat McCormack has managed in each of his last three campaigns at Fulham and Leeds United.
Though the Scotland international turns 30 in August, he would improve Brighton whichever division they are in next year.
According to Sky Sports, the Sussex side's promotion rivals Middlesbrough made an £8 million cash-plus-player bid for McCormack in January, but later signed Blackburn's Jordan Rhodes instead.