Gordon has warned that players could be distracted if the off-field problems are not sorted before the first game of the tournament against France on February 5.
He told Sporting Life: "The goings-on behind the scenes at Murrayfield have obviously been a topic of conversation among the players all week.
"The political situation has not really affected us on the playing front yet, but there are genuine worries in our group about the possible knock-on effects.
"There is always that problem if you work for a company where there is constant strife and battling for boardroom supremacy.
"There is always the chance of this ripple effect going through the whole of the SRU.
"We players would rather see it all sorted out sooner rather than later.
"It is important to ensure that the on-field performances are what you read about in the papers, instead of what is happening off the field.
"We certainly don't want to go into press conferences in the lead-up to the start of the Six Nations to talk about politics at the expense of what we are capable of achieving against France in the first game at the Stade de France.
"It is important for the whole matter to be sorted out quickly and for the SRU to move forward as an organisation, and on the playing front."