The Newcastle United winger is among the players Chelsea have monitored ahead of the summer transfer window as the club prepares to strengthen its attack.
But sources indicate their current sporting situation is going to significantly weaken their chances of completing such a deal.
Chelsea have long-term interest in Gordon, but are understood to have made fresh explorations around how they could position themselves to sign him, if he is to be available on the market when it reopens in June.
However, Bayern Munich are currently leading the race for his signature, and there is becoming a realisation internally that the club are no longer viewed as an automatic destination for Europe’s top players.
That concern stretches beyond Gordon as they plot ways to strenghten the squad.
After a disappointing end to the campaign and uncertainty over the ongoing project, Chelsea are aware that convincing elite-level players to join the club has become considerably more difficult than in previous years.
Sources suggest Gordon does not currently see Stamford Bridge as the most attractive option available to him, with Bayern able to offer greater stability, a clearer sporting structure and the guarantee of competing for major honours.
While they are top of the Bundesliga and have narrowly missed out on a place in the Champions League final, Chelsea have slumped to ninth place in the Premier League, do not have a permanent manager, and need to win the FA Cup final to salvage their campaign.
Insiders suggest Chelsea should be expected to pursue a new winger, centre-back, central midfielder and striker during the upcoming transfer window.
And after spending heavily on emerging talent in recent years, the club are now looking to target more established players capable of making an immediate impact.
Their interest in Gordon fits with the new vision but their status is a problem as Bayern attempt to land him instead.
And there is some concern that their current league position and wider instability could become a recurring obstacle in negotiations for other priority targets this summer.