Valencia, who have reached the Copa del Rey final and the quarterfinals of the Europa League, have Champions League qualification in their sights after climbing up to fifth in the table on 46 points, one behind fourth-placed Getafe.
The centre-back is contracted to the European champions until the summer of 2023.
The 25-year-old has established himself as one of the finest defenders in Europe, but rumours have emerged suggesting that Varane is looking for a new challenge, having enjoyed many successful years with Los Blancos.
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Kovacic has made 41 appearances, without scoring, since arriving at Stamford Bridge on a season-long loan deal from Madrid last August.
Varane has been linked with moves to Manchester United and Bayern Munich, but it is understood the World Cup victor is first weighing up whether he wants to stay at Madrid before deciding on his next destination.
"I don't want a Madrid without Varane", he said.
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"You have to have personality for that and to accept what people want".
"He has won everything that you can at Real Madrid, he has the feeling that he has done what was to be done over there, and there could be a new cycle".
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Many read this as Zidane beginning the process of convincing Pogba to leave United for the Bernabeu, but could Varane moving in the other direction could be seen as payback for those comments?