Mo Farah, Katarina Johnson-Thompson, Laura Muir and Adam Gemili are among those listed as claimants in a legal letter sent to the body.
The athletes argue an International Olympic Committee rule over individual sponsors reduces potential earnings.
The BOA said it is seeking to understand the athletes’ concerns.
Athletes competing in the Olympics are currently bound by the IOC’s ‘Rule 40’, which protects the exclusive rights of official Games partners but prevents athletes promoting their own sponsors.
But top British athletes believe it unfairly prevents them from cashing in on the biggest moment of their sporting careers.
The BOA said it only learned of the legal challenge through the media and is attempting to understand who it is negotiating with – “athletes, agents or commercial organisations”.
The association said it is looking for a positive outcome that “balances the desire for individual athletes to maximise their personal sponsorship revenues with the need to preserve and enhance a system that has collectively sold rights for the benefit of the whole of Team GB”.
It added that includes “smaller sports and less high-profile athletes”.
The BOA said a positive meeting was held with athlete representatives last week, but continued: “Despite those encouraging conversations, we have been dismayed by the ongoing legal tactics being conducted in the background, which in no way reflects the spirit of the discussions held.
“Therefore we have been forced to respond fully and robustly to the legal challenge and have done so in the best interests of all of the athletes we serve and the BOA – a not-for-profit independent organisation that receives no taxpayer or Government funds.
“All monies raised by the BOA are prioritised towards providing athletes with the best support in the performance environment. In the four-year period to Tokyo 2020 we will have taken over 700 athletes to nine multi-sport events, including youth Olympic Games and both senior winter and summer Games.
“We reiterate that it is clearly not in the interest of any party to enter into a protracted legal dispute ahead of the Tokyo 2020 Olympic Games.
“As such, we continue to act in good faith and make ourselves available for further discussions with a strong desire to find a positive solution for the benefit of all athletes through constructive, open and transparent dialogue.”
Gemili, who competes in the men’s 100m and 200m, told the BBC last month that the rules limiting sponsorship were “ridiculous, unjust and unfair”.
“For us it’s about creating the opportunity for every single athlete to go out there and create their own marketing opportunities so they don’t have to work a full-time job,” he had added