According to Don Balon, Suarez has learned United’s Champions League elimination has spurred Real president Florentino Perez into action.
And Perez is apparently hoping to tie up a deal for the stopper as soon as possible.
Real are said to be willing to meet the £89m (€100m) asking price United have slapped on De Gea.
And Don Balon claim United will then use that money to launch a raid on Barcelona for Ter Stegen.
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Luis Suarez has learned Manchester United want Marc-Andre Ter Stegen if they lose David De Gea
Ter Stegen reacts to Barca fans booing Andre Gomes
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Barcelona star Marc-Andre Ter Stegen has forged a reputation as one of the world's top goalkeepers
United are supposedly eager to maintain their run of making big-name signings, with the German fitting the bill.
And that information has come as a blow to Suarez, who’s 'warned' Barcelona chiefs about the prospective transfer chain reaction.
Barcelona might not just have to stave off interest in Ter Stegen from United though.
Paris Saint-Germain are keen on the 25-year-old as they look for an upgrade on Alphonse Areola and Kevin Trapp.