"Those in charge of Bayern Munich condemn this outrageous media speculation, which is not based any facts, in the strongest possible terms," said the Bavarians in a statement.
"We protest against this type of gossip journalism, which we will examine legally and take action against."
"Bayern Munich have the fullest trust in Jupp Heynckes and his work."
Bayern, second in the Bundesliga, have dropped seven points behind leaders Borussia Dortmund with 10 matches to play, having taken only 11 points from a possible 21 since the mid-season break.
They also face an uphill struggle in the Champions League after losing 1-0 away to FC Basel in their first leg of their round-of-16 tie.
Bayern's Allianz Arena will host the final, adding to the pressure on the team to go all the way.
Heynckes, 66, returned for a third stint at Bayern this season and was given a two-year contract.
He replaced volatile Dutchman Louis van Gaal who was fired last April having had his contract extended until 2012 earlier that season.
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