After the sacking of Roy Hodgson as England manager, Sunderland want to keep hold of their current boss.
There have been several deals for players in recent weeks with Vito Mannone the latest player to commit to the club, following Patrick van Aanholt and Jermain Defoe in agreeing new deals.
Midfielder Jan Kirchhoff is also in line for a new contract following some impressive displays after arriving from Bayern Munich in January.
Allardyce has been one of very few English names linked with the national side job following the sacking of Roy Hodgson after England's embarrassing exit from Euro 2016 at the last-16 stage of the competition to Iceland.
The Sunderland Echo's report says that securing the future of their manager has been on the agenda for a number of weeks, and recent speculation about England will only add to the urgency to tie Allardyce down to a new deal at the Stadium of Light.
It also states that Allardyce has made no secret of his desire to manage the national side, but after guiding the side to safety to last season - with the hope of kicking on this term - there will be no wish on the club's part to see him leave.
It is of little surprise that they want to tie him down to a new deal. After several years of flirting with relegation to the Championship, they have a real chance to have a really stable season under their manager, and even push for the top half rather than having to rally towards the end of a campaign in order to secure their safety.