Maddison has almost sealed a £40million move to Spurs with only medical tests to be done and the documents to be signed.
The English midfielder has just come off the back of a Premier League campaign where he registered 10 goals and nine assists.
However, this was not enough to help Leicester stay in the top flight as they were relegated to the Championship.
The north London club are set to sign the 26-year-old in a cut-price deal, £20m below the Foxes' initial £60m value.
Winks, meanwhile, has been at Tottenham for his whole career but he spent last season out on loan to Sampdoria.
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He graduated from the north London side's academy but has fallen out of favour over the last few years due to injury problems and the signings of Pierre-Emile Hojberg, Yves Bissouma and Rodrigo Bentancur.
Leicester City and Tottenham have reportedly agreed a deal worth up to £10 million for the midfielder.
However, Maddison and Winks will not be separated from their teammates for long as the two clubs play each other in a pre-season friendly on July 23.
The match will take place in the Rajamangala stadium in Bangkok, Thailand, as the clubs get ready for the 2023/24 campaign
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As well as the arrival of Maddison, Tottenham may also have several other debutants.
Italian goalkeeper Guglielmo Vicario has signed on a five-year deal from Empoli in a transfer worth £17.2m.
And they are also rumoured to have interest in centre-backs Micky Van de Ven of Wolfsburg and Bayer Leverkusen's Edmond Tapsoba.
There will also be a lot of attention on Harry Kane and whether he is still a Tottenham player when the game is played.
Bayern Munich have bid £60m for the England captain but Spurs currently look set to reject any offer for their record goalscorer.
And Leicester may also have more than just Harry Winks's debut to look forward to.
The Foxes are rumoured to be interested in both Wolves centre-back Conor Coady and Swansea striker Joel Piroe as they attempt to win promotion back to the Premier League.