The 23-year-old has been in impressive form for the Foxes this term, scoring 13 times and registering four assists in 34 appearances, including nine goals in 24 Premier League outings.
According to The Mirror, both Man United and Liverpool have had the Englishman watched, but Leicester are determined to tie the attacker to a new long-term contract.
The report claims that the Foxes are currently in 'advanced talks' with Barnes over a fresh agreement which could make him one of the top earners at the King Power Stadium.
Barnes's existing deal with Brendan Rodgers's side still has more than three years left to run, but the attacker's salary allegedly does not reflect his role in the squad.
The Leicester academy product made his England debut against Wales last October.