Trippier has enjoyed a very positive 12 months or so. His final appearance in a Spurs shirt came in the club's 2-0 loss to Liverpool in the Champions League Final.
Trippier may well be able to extol the virtues of leaving Spurs for Madrid, pushing Daniel Levy to try and find a replacement in the market.
The England global had been expected to leave North London this summer and was initially linked to a move to Serie A with Napoli and Juventus mooted as potential suitors.
Ornstein has confirmed that Arsenal is set to see off Tottenham in the race to sign 18-year-old St Etienne defender William Saliba.
Trippier moved to Tottenham from Burnley in 2015 after an impressive spell in the side at Turf Moor.
And after putting pen to paper on a three-year contract, Trippier got involved with his new team-mates straight away by training with Diego Simeone's men on Wednesday evening.
The Spanish club have also secured Joao Felix for £113m from Benfica and Marcos Llorente from Real Madrid, while selling Antoine Griezmann to the champions, Barcelona, for £107.7m.
Dutch striker Vincent Janssen has been told he is free to leave Spurs this summer.
Ben Davies and Eric Dier also miss out as they recover from injury ahead of a Premier League season that starts on August 10 with the visit of newly-promoted Aston Villa to the Tottenham Hotspur Stadium.