Calderon told BBC Radio 5 Live: "I know that this morning the president [Florentino Perez] called Zidane to ask him back; he said not now. He has left open the possibility of coming back in June."
Zidane quit the club last summer after delivering a third consecutive UEFA Champions League title.
Then-Spain boss Julen Lopetegui was appointed to replace him, but he was sacked at the end of October after a record of six wins, six losses and two draws.
Santiago Solari was then handed the reins and made permanent manager after winning his four matches in charge as a caretaker.
However, the Argentinian has found it difficult to build on that early momentum, and Real's struggles have come to a head in the last week, as the Guardian's Sid Lowe noted:
A 3-0 defeat to Barcelona in the second leg of the Copa del Rey semi-final on February 27 was followed by a second consecutive defeat to the Catalan giants in La Liga on Saturday, which left Los Blancos 12 points behind the leaders.
On Tuesday, Real were humiliated 4-1 by Ajax to end their hopes of a fourth consecutive Champions League title. The result overturned Los Merengues' 2-1 victory in the first leg and knocked them out of the tournament at the last-16 stage.
Zidane orchestrated an impressive turnaround at the Santiago Bernabeu when he replaced Rafa Benitez in 2016, and in his first full season, he inspired Real to win just their second La Liga title in nine years.
La Liga writer Andrew Gaffney isn't convinced by the possibility of him returning, however:
Given Benitez had won 17 of his 25 matches in charge, there wasn't an enormous amount of work needed when Zidane took charge the first time because the team were already performing fairly well.
However, Real now need to move on from Cristiano Ronaldo following his departure to Juventus last summer and transition to a new generation of stars, given Sergio Ramos will be 33 this month and Luka Modric turns 34 in September.
Doing so will be an enormous challenge and very different to the one Zidane faced in his first spell at the club, so there's no guarantee he'd be able to replicate his earlier success.