And England captain Dylan Hartley is also closing in on a return following a back injury.
However, JJ Hanrahan is set to be out for a while yet as he continues to recover from a broken ankle.
Hanrahan has yet to feature this season after sustaining the problem in a pre-season friendly at Ulster, while Day has also been unable to play a competitive game due to a ruptured bicep.
And Mallinder said: “JJ Hanrahan’s a little bit further off because he broke his ankle, but Christian Day is making progress and should be back in the next couple of weeks.”
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On Hartley, he added: “Dylan is making good progress, he’s training, he’s doing weights, he’s running so he’ll be close for this week (against Montpellier).”
Calum Clark was forced off after taking a knock to the head during the defeat at Harlequins on Saturday.
But Mallinder said: “He did get a bit of a blow to his head so we took him off, but I think he’s okay.”