France international Dembele joined Barcelona from Borussia Dortmund for a fee of £97million in 2017, which was then a LaLiga record.
The enigmatic winger has failed to justify his price in Spain, with a mixture of injuries and form seeing him limited to 120 appearances and 30 goals in five seasons.
Recently appointed manager Xavi Hernandez is desperate to hold on to the still highly-rated 24-year-old, but things may be out of his control with Newcastle making a contract offer Barca can't match.
Reports in Spain claim Dembele will be offered €15m in wages [over £250,000 per week] and a €15m [around £12.7m] signing bonus, with the Frenchman's contract set to expire in the summer of 2022.
The Magpies can officially sign Dembele to a pre-contract agreement on January 1 ahead of a summer move, and the deal would represent a huge statement of intent from the club's new ownership.
Newcastle were purchased by Saudi Arabia's Public Investment Fund in October, making the club the richest in the world with the country's Crown Prince, Mohammad Bin Salman, worth as estimated £320billion.
Conversely, Barcelona are in a financial crisis due to the COVID-19 pandemic, with club president Joan Laporta claiming their debt totals £1.15billion.
Mundo Deportivo also report there is interest from fellow Premier League side Manchester United in the chase for Dembele, but Newcastle's bid may be unrivalled.