PA understands Trippier is set for a medical in Spain on Wednesday ahead of a potential move to the LaLiga outfit after a deal with Spurs was agreed.
Also last month, Rose admitted that he did not know whether he would still be with Spurs next season. His final appearance in a Spurs shirt came in the club's 2-0 loss to Liverpool in the Champions League Final.
But it has been claimed Tottenham ignored the temptation to sign the attacker and opted for a straight cash deal to sell the defender this summer.
There had been an agreement with the centre-back since May but negotiations with Espanyol have been complicated with the Catalan club looking for €35m since Real Madrid own 50 percent of Hermoso's rights and will get half of the transfer.
The England left-back has made it clear he is unhappy with Spurs' pay structure.
The Danish global has failed to sign a new contract at Spurs, meaning he will be out of contract next summer.
The way the Telegraph tell the story, that may depend on Danny Rose. The latest development, that for the time being will see him prepare for the new season without his team-mates, demonstrates that club and player both see this as potentially the end of their 12-year association.
"Ben Davies, Eric Dier and Cameron Carter-Vickers will continue their rehabilitation at Hotspur Way", said a statement on the official Tottenham website.
Along with Vincent Janssen and Georges-Kevin Nkoudou, £60,000-a-week (Spotrac) England global Rose has "been granted additional time off in order to explore prospective opportunities with other clubs".
'Serge Aurier, Davinson Sanchez and Victor Wanyama will return to Enfield to start pre-season training next week following commitments with their national teams at summer tournaments'.