Antonio Conte has made just two signings so far - N'Golo Kante and Michy Batshuayi - and is desperate to bolster his squad before the transfer window shuts later this month.
The Blues want to land Rodriguez, who is available having fallen down the pecking order at the Spanish giants.
Rodriguez starred at the World Cup in Brazil two years ago but has endured a difficult two years since his move from French side Monaco.
The Colombia international was omitted from Zinedine Zidane's starting line-up for the Champions League final last season and could now be set for a big-money move to Stamford Bridge.
Etienne Capoue gave the Hornets a shock lead before sub Batshuayi and Diego Costa struck to earn all three points.
"I’m pleased for the substitutes that came off the bench. They showed great attitude and commitment with Cesc Fabregas and Michy Batshuayi making a real impact,” Conte told the BBC.
"We all know Cesc’s quality, he’s a great player but it’s important to understand that we are at the beginning of the season and I am looking for the right balance."
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Chelsea boss ponders striker partnership
Conte is considering whether to field Costa and Batshuayi from the start in the future.
The duo linked up for the second time in as many games during Chelsea's win over Watford.
Batshuayi has made a huge impact from the bench in both games - and Conte has refused to rule out selecting the youngster alongside Costa in attack.
"Costa is for us an important player. During the game I can see both the positive things and negative things (said about Costa),” said Conte.
“But it’s not only about Diego. Batshuayi is a young player with a great potential. He can improve a lot.
“They can play together, not only during the game but also from the start.”
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