The team has won just four of their last nine games, allowing defending champions Borussia Dortmund to open up a seven-point gap over second placed Bayern at the top of the Bundesliga.
As speculation mounts, German daily Bild claimed Wednesday that Heynckes, whose contract expires in June 2013, could be replaced by Borussia Mönchengladbach coach Lucien Favre or Hanover 96 boss Mirko Slomka.
But club bosses have moved to dispel the reports. "Bayern Munich have full confidence in Jupp Heynckes and his work," they said in a statement.
There has already been some media speculation about the early resignation of Jupp Heynckes, and rumours are circulating that the club has held discussions about the coaching position – which has been filled by six different people in the past five years.
Bayern have fought against this speculation, saying that, "those in charge of Bayern Munich condemn this outrageous media speculation, which is based on no facts, in the strongest terms.”
"We protest against this type of 'gossip journalism' and will be investigating our legal options in the future."
Bayern, who suffered a two-nil defeat at Bayer Leverkusen on Saturday, face a make-or-break fortnight as they need to overturn a one-nil defeat from the first leg of their Champions League Round of 16 clash when they host FC Basel on Tuesday.
They then have a German Cup semi-final at Mönchengladbach, who have beaten them home and away, on March 21 and need to close the gap behind Dortmund in the league.