Representations will be made to US authorities over a UK resident held at Guantanamo Bay, a QC acting for the government has told the High Court.
The three men's lawyer claims they risk further ill treatment
Christopher Greenwood QC said facts in Bisher al-Rawi's case made the foreign secretary decide on "a specific, security-related request" to the US.
Mr al-Rawi, Jamil el-Banna and Omar Deghayes have asked the court to force Jack Straw to press for their release.
The judges are expected to give their decision in the next couple of weeks.
They reserved their judgement after the two-day hearing.
The government has always maintained that it cannot help the men as they are not British nationals. The three men are believed to be among at least five UK residents still held at the US-run detention camp in Cuba.
The case of Mr al-Rawi, an Iraqi-born businessman who has lived in the UK since 1985, had been "reconsidered separately" by Mr Straw, the QC told the court.
Lawyers for Mr Al-Rawi have argued that he helped British intelligence.
He said the facts in his case, which could not be gone into in open court, had led Mr Straw to conclude representations should be made on his behalf to the US government.
Mr Greenwood told the court the actual form which the intervention would take had not yet been decided.
The QC told Lord Justice Latham and Mr Justice Tugendhat at the London court there were currently no plans to make "general requests" on behalf of Mr el-Banna and Mr Deghayes.
"To put it succinctly and candidly, the likely reaction to a security-related request may be different from the reaction to a general request," he said.
In documents previously submitted to the court, Mr al-Rawi and Mr el-Banna were alleged to have connections with al-Qaeda through radical Muslim cleric Abu Qatada.
However, lawyers for Mr al-Rawi have consistently argued he had contact with Qatada "expressly approved and encouraged by British intelligence".
Mr al-Rawi maintains intelligence staff had told him they would help him if he ever ran into trouble.
Lawyer Timothy Otty, appearing for all three men, told the court on Wednesday that documents established "communications" between British and US security services relating to Mr al-Rawi and Mr el-Banna before their arrests.
Mr Otty said: "We will certainly be contending there has been real injustice, and there is a causal link on the part of those acting for the UK in that injustice."
Amnesty says Mr al-Rawi and his friend Mr el-Banna, a Jordanian refugee who had been living in London, were arrested in November 2002 at Banjul airport, during a business trip to Gambia, on suspicion of having links to terrorism.
Libyan-born Mr Deghayes, 36, of Brighton, has been held at Guantanamo for three years and was on a hunger strike, Mr Otty said.
He was arrested in Pakistan and accused of committing terrorist acts against the US, but his lawyers claim it is a case of mistaken identity.
Mr Deghayes fled Libya for Britain in the 1980s after his father was assassinated. He was granted refugee status in the UK, where he was educated and applied for British citizenship.
Mr Otty had also told the court there was "compelling evidence" the three men had been "severely tortured" at Guantanamo and were at "real risk" of further ill treatment.
Mr Greenwood told the judges on Wednesday the government was "attaching considerable weight" to the US denial that torture or inhuman treatment had taken place at Guantanamo Bay.
The government would "certainly not accept that there was compelling evidence that the men have been tortured", he added.