According to a report in The Times, Ramos is a candidate to replace Mourinho, who was sacked by Chelsea on Thursday.
“Some people have mentioned Juande Ramos,” said Redknapp jokingly on BBC Radio 5 live. “He did great at Tottenham before I went there! I took over from him and the club had two points from eight games.”
Ramos was appointed the Tottenham manager in October 2007 after achieving success with Sevilla, but he struggled to make a huge impact in England.
The Spaniard was sacked as the Spurs boss in October 2008, with Redknapp subsequently taking over the reigns at White Hart Lane.
Under the Englishman, Tottenham went onto achieve big success in the Premier League and also featured in the Champions League.
Ramos, though, did not find himself out of work for long after getting the boot at Spurs. The 61-year-old got the biggest job there is in club football when he was appointed the Real Madrid boss in December 2008.