The Scot has been linked with the vacant manager's job at White Hart Lane, along with Wigan boss Roberto Martinez and former Chelsea manager Andre Villas-Boas, following confirmation in the early hours of Thursday morning that Redknapp had been sacked.
Moyes told BBC Radio 5 Live: "All I can say is that I have had no contact and if I had had any I would have told my chairman (Bill Kenwright).
"I hope to meet all my ambitions at Everton but you never know in this game.
"I came back from holiday and found out about Harry and I feel sad for him because I feel he has done a good job."
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Moyes has battled against a restricting budget at Everton but last season took the club to sixth in the Barclays Premier League, one place above bitter vials Liverpool.
Redknapp left Tottenham despite taking the club to fourth spot.
The 65-year-old took charge of Spurs in October 2008, transforming their fortunes from a side struggling in the Premier League when he joined them to title contenders at one stage last season.
Redknapp led his side into the Champions League in 2010-11 but last season's fourth place was not good enough for a repeat visit after Chelsea took the spot courtesy of their penalty shoot-out win over Bayern Munich in this year's final.
Redknapp was linked with the England post prior to Roy Hodgson's appointment, and Tottenham's early-season form fell away and they ultimately lost out on Champions League football once again.