It was reported last week that MacPhee was a leading contender to take over the Indian Super League side.
After taking the weekend to think things over, while speaking to manager Craig Levein and owner Ann Budge, the 38-year-old decided to remain at Tynecastle.
However, Pune City have now claimed in a Facebook post on their official page that no offer was made.
They said: “In light of recent media reports publishing that an interest and subsequent offer to Heart of Midlothian assistant coach Austin MacPhee, FC Pune City hereby wishes to state that this information is absolutely untrue.
“FC Pune City has made no contact whatsoever or any kind with the club or coach or to any agents or representatives.”
Hearts announced on Monday evening that MacPhee had received a “managerial offer” which he had turned down.
MacPhee told the club’s website: “It was an interesting offer from the Indian Super League side and one I thought very seriously about.
“However, at this moment in time it is probably not the right opportunity for me and I am delighted to be continuing my work at Hearts.
“There is a lot to feel positive about as we head into the new season and I’m very much looking forward to the campaign ahead.”