The Serie A outfit were linked with a move for Witsel earlier in the transfer window, but failed to agree a fee with Zenit Saint Petersburg.
Last week Milan CEO Adriano Galliani suggested the club had moved on from the Belgian midfielder, saying: "No [we won't sign Witsel], that's enough now.
But Italian paper Corrierre dello Sport suggest that Milan have now altered their stance.
It is claimed that they have begged Witsel not to commit to Chelsea until August.
A defender remains a priority for the San Siro outfit but they hope they may still have the funds to complete a deal for Witsel once that is out of the way, according to the reports.
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