Barca and the Germany goalkeeper pulled back from talks earlier this week, with negotiations hitting an impasse.
However despite the stand-off, reports Mundo Deportivo, there's a confidence at Barca's end of the table of an agreement being struck.
A board source said: "Ter Stegen will renew four or five years. It's certain."
Barça have already met four times with the goalkeeper's management. At the last meeting, held in early March, an offer was tabled to 2024 at the rate of €6.5m-a-season net, plus bonuses based on personal and team objectives.
But the German rejected the proposal, knowing the club has recently renewed several players who have fewer minutes than he and who will earn more money.
Ter Stegen says he just wants to feel valued as the first-choice that he is.
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