The pair have pulled out of this week's ATP tournament in Stockholm while Venus heads back to London to rests a tight Achilles this week.
But there is a chance he won't head back to New Zealand on the 20th to take up his MIQ spot after possibly qualifying as alternates for the World Tour Finals in Turn thanks to the Paris victory.
Venus and Puetz are up to 11th in the race and while the top eight teams are finalised for Turin, Venus and Puetz are effectively the second alternates because Filip Polasek, who is playing with Venus' former partner John Peers, had already qualified with Croatia's Ivan Dodig.
So with Peers ineligible, Venus and Puetz are second alternates. They now have to wait to see what happens in Stockholm this week where the pair immediately behind them, Ariel Behar and Gonzalo Escobar, will have a chance to go ahead of them if they win.
The chances of Venus and Puetz getting to play in Italy would be slim as second alternates, but they would pocket around $25,000 each just for turning up.
To even be in the position they are in is remarkable given they have played only half a season together, starting after the French Open where they reached the semifinals on grass in Halle, Germany.
They then lost in the second round at Wimbledon before going to Hamburg and winning the European Open on clay. Venus then went collected Olympic bronze in Tokyo with Marcus Daniell for New Zealand.
Venus then had to pull out of their first-round match at the US Open when Puetz suffered a side strain and spent a month in Germany to recuperate. However, they clicked immediately on their return and reached the semifinals at the Indian Wells Masters, a tournament rated as the unofficial fifth major.
Venus says what they have achieved in just a few months together has given them a lot of optimism for the 2022 season.
"Considering we played half the year, and I had a niggle for a while and Tim tore his oblique, to finish where we have is promising and we have felt really good, especially the last few weeks in what we are doing and getting more comfortable and trusting each other out there."