The 77-year-old former Dunedin resident left St Augustine, Florida, on November 9 on his second attempt to break the Bermuda to Bermuda record of 150 days, which was set by the late Dodge Morgan aged 56 in 1986.
Dr Paris is now about 500km off the coast of Rio de Janeiro, Brazil, and is preparing to head east towards the southern tip of South Africa.
It has been about 20 days and 6000km since he rounded Bermuda, and he calculates he is about a day ahead of where Mr Morgan was during his record attempt.
''He [Dodge] did better through the doldrums than I did. He shot through with favourable winds while I had some windless times and some time out for repairs.
''At this point, Dodge is 249 miles [400km] northeast and behind me - a little more than a day, but he is east of me and will stay that way for a while.
''Now, we enter an area off the coast of Brazil where we will start to lose the easterly trade winds and have many variables, along with squalls in the early morning and at dusk.''
Dr Paris said it was in these waters that Kiwi Spirit received most of its damage last time, which ultimately forced him to abandon his record attempt.
''So I shall be sailing more conservatively for the next 10 days and expect Dodge to gain and pull ahead of me.''
It would be interesting to compare Kiwi Spirit's speeds with Dodge Morgan's when he reached the Southern Ocean, he said.
''Of course it's early days, but it's a better start than last time.''
Dr Paris also aims to beat the fastest solo circumnavigation record from China to China, which was completed last year in 137 days by Yuan Chang.
At the very least, if he completes the non-stop voyage, he will set a record for being the oldest person to solo-circumnavigate the globe, and will set a record for being the fastest person to sail from St Augustine to St Augustine.