Red Bull motorsport boss Helmut Marko told Germany's Bild newspaper: "The idea of Mercedes is finished. We are now focusing elsewhere."
Team principal Christian Horner said he was doing "necessary due diligence" in talking to other manufacturers.
With their partnership with Renault disintegrating, the team may be forced to switch to Ferrari engines.
Mercedes are understood to be against supplying Red Bull - who are contracted to Renault until 2016 - because they do not want to help a strong rival become more competitive.
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The German giant is also concerned about what it and many other F1 insiders perceive to be Red Bull's history of antagonistic relationships with engine partners.
Red Bull's relationship with Renault has been difficult for some time, and appears to have become untenable in recent months as the team's frustrations with the lack of competitiveness of the French engine boil over.
Honda is the only other manufacturer in F1, but partner McLaren would almost certainly exercise their veto over any potential deal with Red Bull, who in any case are not believed to be interested in a deal with the Japanese company at this stage.
Renault, which supplies only Red Bull and sister team Toro Rosso in F1, is in the final stages of negotiations to take over the financially troubled Lotus team, although no deal has yet been completed.
Ferrari team principal Maurizio Arrivabene said the Italian company was prepared to supply Red Bull if necessary.
He said he was not concerned about their reputation for being able to build highly-competitive chassis in F1, led by their design chief Adrian Newey.
Arrivabene said: "In theory they have big names, with Newey as chief designer and it is easy to think that if you give them the engine they will build a scary chassis, which means they will be really competitive.
"Concerning my team, my engineers and aerodynamicists know their own jobs. For that reason I don't have a problem, and competition is nice when you have a stronger competitor.
"This doesn't mean tomorrow morning we will give our engines to Red Bull or Toro Rosso.
"But I don't see any kind of problem to give our engine to any other team or be scared of the competition before they start.
"This is not the right spirit of competition or what Ferrari represents. We fight with everybody."
Red Bull have said that their hopes of securing a Mercedes engine supply in 2016 are now over.