(CNN) NATO is considering a recent request by a UK member of parliament and chair of the foreign affairs committee to name the alliance's new billion-dollar headquarters building in Brussels in honor of the late US Sen. John McCain.

NATO spokesperson Oana Lungescu told CNN that the request had been received by NATO Secretary General Jens Stoltenberg and "will be considered carefully."

The proposal was endorsed Tuesday by Stoltenberg's immediate predecessor Anders Fogh Rasmussen as well as two additional former Secretaries General, Lord George Robertson and Javier Solana.

"Despite his being a US Senator, across Europe we all felt that John McCain III was one of our own," the three men wrote in a letter Thursday to The Times newspaper of London.

"We urge NATO to repay this lifetime of service to its mission by naming its new Brussels headquarters after Senator McCain," they added.

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