Red Devils boss Jose Mourinho is reported to be a fan of the Brazil international and tried to sign him when he managed Real Madrid.
United boss Jose Mourinho is also believed to be a big fan of the Brazil international, and even made advances to sign him when the Portuguese was in charge of Real Madrid.
Wagner Ribeiro, Moura's agent, believes the interest both United and Mourinho have shown in Moura has not lessened and, with Mourinho now in charge at Old Trafford, Ribeiro expects further advances for his client in the future.
"Who called Lucas Moura there [to Real Madrid]? It wasn't Florentino Perez who wanted Lucas Moura, it was Mourinho," he said.
"Mourinho was and is passionate about Lucas Moura. So much so that now at Manchester he wants Lucas as well."
Former Sao Paulo man Moura has been in great form for PSG this season, with five goals from his first seven games as he continues to show why he was such a highly regarded talent when he joined the club.
Such a contribution is needed at United, who are in turmoil at the moment having lost their last three games in all competitions and looking well below their best.