The 27-year-old has been training with the Premier League side, and the Daily Mail report that he impressed manager Javi Gracia enough for the club to enter into contract talks with his representatives.
Rodwell is currently a free agent after cancelling his £73,000-a-week contract with Sunderland last month, and is said to have spoken to clubs in the United States, the Netherlands and Italy over a potential move.
Having been relegated twice during his time at Sunderland, Watford have offered him a Premier League lifeline as he looks to finally get his career back on track.
The former England man impressed in the early years of his career, breaking into the first team at Everton before earning a move to Premier League rivals, Manchester City.
His career went downhill following that move, as he fell out of favour and was moved on to Sunderland. During his time in the north east, he faced two relegations and also fell out of favour with the Black Cats.
Despite having a Premier League winner's medal and over 150 Premier League appearances, his career never hit the heights he was tipped for as a youngster at Goodison Park.
He has 213 career appearances to date, scoring just 17 goals from his central midfield role. He also has three caps for the England national team, with two coming in 2011 and the third in 2013.
Watford are also said interested in signing Egypt international Tarek Hamed, who featured for his country in all three of their games at this summer's World Cup. The 29-year-old is expected to cost the Hornets a modest £1.5m.