Chief among their targets is Tottenham's Christian Eriksen. The Mirror claims that Julen Lopetegui wants Eriksen to lead his midfield in the years ahead, but he may have to wait until January or next summer.
AS claims that Thiago would like to be reunited with his former national team manager Lopetegui, who called him up to Spain's World Cup squad before he was dramatically sacked on the eve of the tournament.
Former Barcelona man Thiago extended his contract with the German champions until 2021 last year but he is keen for a return to La Liga, and Bayern chairman Karl-Heinz Rummenigge has indicated that the club may allow midfielders to leave.
"Right now we're seeing whether any players want to leave. We have nine players [in midfield] and only three or four spots to go around," he said.
Thiago is valued at €60m but Bayern's eagerness to make James Rodriguez's loan move permanent may help in facilitating a more easy transaction.
An alternative option is Miralem Pjanic. The Bosnian international has had admirers in the Spanish capital since his Lyon days and would also be a good replacement for Kovacic.
However, Real expect that Juventus will demand an asking price close to €80m for Pjanic. They are unlikely to pay that much, particularly as Eriksen is their preferred long-term option.