Thompson, who was Houllier's assistant manager at Liverpool, told Paddy Power: "In the final game of the 2002/3 season, it was a shoot-out between Liverpool and Chelsea for the last Champions League place.
"After the game, as Chelsea were doing a lap of honour, Gerard Houllier said to me that Terry was a bit of a player. I agreed, adding I didn't think they'd offered him a contract.
"After, we sent one of our coaches in to the players' lounge and asked John for his agent's phone number. John said: 'I'll do more than that, here's my personal telephone number, ask him to give us a call'.
"And a couple of weeks later, Abramovich took over, and his first dealings were signing Terry and Lampard to big contracts – so we were that far away from getting him."