The England Under-21 international is a key part of Gus Poyet's plans for next season.
Wickham is entering the final year of his contract at the North-East club, but hartlepoolmail.co.uk reports that he has a "concrete place" in manager Gus Poyet's plans for next season.
The England Under-21 international impressed during loan spells at Sheffield Wednesday and Leeds United last season, and netted twice against Leicester while playing for Wednesday.
He then returned to Sunderland and scored five goals in the club's final six games of the season, playing a pivotal role in their escape from relegation to the Championship.
Leicester have signed Marc Albrighton, Matthew Upson, Jack Barmby and Ben Hamer this summer, and manager Nigel Pearson was supposedly lining Wickham up as his top target.
It appears now, however, that Sunderland will look to lock the striker up with a long-term deal after he finally fulfilled the potential that led them to sign him for £8 million in 2011.
"We have had an interest in a number of players and some haven't worked out for various reasons. The players we are currently interested in, if we can achieve that then fine," he told the Leicester Mercury.
"We will continue to strengthen the squad before the season starts, if and when we can. If players become available that we feel are right for us, I know we have the ability to achieve a certain amount of success in that regard.
"Sometimes you get to a value with a player where it no longer becomes doable. I am prepared to pull the plug if I think we are not going to get the right players at the right price."
The club have also been linked to Tours striker Andy Delort, and are thought to have had a £7 million bid for Leonardo Ulloa turned down by Brighton& Hove Albion.