Personal injury lawyer Sally Moore said a couple of people had asked for legal advice about their options.
All 136 passengers were evacuated safely when the Boeing 777 lost power on approach to the west London airport.
BA said it was in discussions with customers about a variety of issues and had offered a fear of flying course.
No-fault basis
Flight BA 38 from Beijing was extensively damaged when it touched down on 17 January.
The Air Accident Investigation Branch (AAIB) has indicated its inquiry into the incident may be focusing on the aircraft's fuel supply system.
A spokesman for BA said: "We are in confidential one-to-one discussions with our customers about a variety of issues.
"We have offered a fear of flying course to those passengers who want to take one. We are in touch with all passengers who were on BA 38."
Ms Moore, a partner at specialist personal injury law firm Leigh Day & Co, said passengers who had been traumatised by their experience could claim up to £85,000 on a "no-fault basis".
She said: "Trauma is another injury. It's compensatable like any other injury, it's just harder to identify.
"We have been asked to advise a couple of people on what their legal remedies might be.
"They are considering their options. We are not acting for them yet."
Praising BA's efforts to assist passengers she said: "Anything they can do now to stop the problem arising is better than a problem becoming entrenched."
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