The newspaper say Spurs fear they will lose Christian Eriksen and Toby Alderweireld because of their respective contract situations and that Danny Rose, Victor Wanyama and Vincent Janssen could also leave.
Eriksen, whose Spurs deal expires in 2020, continues to be linked with Real Madrid, while a clause in Alderweireld’s contract could lead to him leaving the club for £26m.
The Mail say Spurs are therefore looking to spend this summer in order to revamp the squad.
As well as Zaha and Mitrovic, they are also said to be eyeing Aston Villa midfielder Jack Grealish, Hull City forward Jarrod Bowen and Valencia’s Carlos Soler.
However, there appear to be stumbling blocks to a deal to sign Zaha and Mitrovic.
Spurs have long been linked with Zaha but Palace are determined to keep him and their valuation of the winger seemingly makes a move very unlikely.
The Mail also reports that Serbian striker Mitrovic could be reluctant to join Spurs as a back-up option for England captain Harry Kane as his first-team opportunities would be limited.