Negotiations over a new deal were put on hold at the start of the coronavirus pandemic but talks resumed with Ter Stegen's agent last month and a loose agreement was brokered last week.
Sources close to the discussions have told ESPN the Germany international's new contract could be drawn up and signed before the end of the month -- and maybe even before next weekend's Clasico against Real Madrid.
Under the terms of the new agreement, Ter Stegen will receive a substantial wage rise in accordance with his increased importance to the side, placing him among the club's top earners.
However, the increase to his salary will be staggered across the five-year deal to help the club manage the financial fallout caused by the coronavirus pandemic. Cost-cutting measures this summer have already seen Luis Suarez, Arturo Vidal and Ivan Rakitic leave the club.
Ter Stegen, 28, had always made it clear to Barca that he wanted to commit his future to the club despite interest from elsewhere.
Sources say Chelsea made the most "serious" move for the goalkeeper, while Inter Milan were keen to do a deal in 2021. There was interest a while ago from Juventus, too, but the Italian champions have not followed up on their initial approach.
Ter Stegen and his young family are settled in Catalonia and he has emerged as a real club man. This week he publicly congratulated Barca's futsal team for winning the European Cup -- a gesture, one source inside the club points out, none of the first team's four captains replicated.
Despite that, he wanted to feel that his role at the club was recognised. Since signing his last deal in 2017, he's seen several new signings join on bigger salaries, while goalkeepers are commanding increasingly large transfer fees -- and subsequently wages -- on the market.
He also wanted assurances that Barca are going to be able to compete for major trophies in the coming seasons, too.
Barcelona, meanwhile, made extending his contract a priority once the transfer market closed last week. President Josep Maria Bartomeu wanted the issue resolved before his mandate ends next year.
To help convince Ter Stegen to renew, the club even asked new coach Ronald Koeman to retain goalkeeping coach Jose Ramon de la Fuente, who's worked with Ter Stegen since he signed in 2014, rather than bring in his own coach.
Ter Stegen, who has made 236 appearances for Barca since signing from Borussia Monchengladbach six years ago for €12 million, has not played yet this season due to a knee injury but is back in light training.