Milan have beaten Serie A's leading pair Juventus and Lazio in the last four days and Pioli -- whose contract runs until the end of next season -- has got his young side playing the high-tempo game often associated with Rangnick himself.
The first reports linking Milan to Rangick surfaced in February when Pioli had been in charge for four months which had included a 5-0 drubbing by Atalanta, Milan's worst defeat for 21 years.
Though Pioli insisted that his young team were on the right track and were not getting the results their performances deserved, the reports continued to swirl.
Pioli, though widely respected, is seen as something of a journeyman. The 54-year-old has been doing the rounds of Italian clubs for nearly 20 years, including Lazio, Fiorentina and Inter Milan, but has never won a major title.
Rangnick, meanwhile, is regarded as a visionary and one of the modern pioneers of aggressive high-pressing football.
On Monday, numerous Italian media reported that Milan had agreed terms with Rangnick, who would be given a wide-ranging role similar to that of an English club manager and which would also eat up the role of technical director Paolo Maldini.
Some reports have suggested that both could get a new role alongside Rangnick.
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The club has not officially commented while both Pioli and Maldini have to field questions about the situation before and after every match.
"I can't waste energy thinking about situations that are not up to me," said Pioli after Tuesday's match.
"I am so happy here, proud and eager to end this season on a high. I like being with my team and whatever will be, will be. I just want to finish the championship well."
Maldini, who spent 25 seasons at Milan as a player and is a club favourite, also tiptoed around the subject.
"I don't know, I want to make it to the end of this season, because we can still achieve the goals we set ourselves. Then the time will come to decide our future," he said.
"Do I want to stay? It's a difficult question: but there will always be a great bond."