In total, he now has five goals and four assists in the Brazil tournament as he aptly fills the gap left by the injury to club and country teammate Radamel Falcao.
The 22-year-old had already been attracting some transfer interest ahead of the World Cup, but his performances at the competition have sent the transfer rumour mill into overdrive.
Sports Mole looks at some of the potential landing spots for the midfielder.
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Rodriguez has admitted that he dreams of playing in Spain during his career, leading to speculation that he could be heading to Real Madrid this summer. Los Blancos already have Isco in their squad, who possesses a similar range of skills to the Colombian, and have been linked with a big-money move for Luis Suarez this summer, but they're not short of resources so could be in a position to make a bid for the playmaker. It would surely be an exciting and tempting move for Rodriguez, who has previously revealed that Cristiano Ronaldo is one of his heroes.
If Rodriguez is keen to play in Spain and win silverware, then Barcelona provides the same opportunities as Real Madrid. Although the Camp Nou outfit have not been linked with Rodriguez as frequently as their El Classico rivals in recent weeks, he would fit nicely into their squad. With Cesc Fabregas having already departed the Catalan giants this summer, and Alexis Sanchez also attracting interest from other clubs, Rodriguez could fill a hole in midfield. At times last season, Barcelona were unable to get the best from Lionel Messi, but the 22-year-old has proved that he is as capable at setting up goals as scoring them, and could potentially form a deadly partnership with the Argentine striker.
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Rodriguez's agent has admitted that he has already held talks with the Serie A side and that other parties are interested. Aytekin Erayabakan told AreaNapoli: "I can confirm that I have spoken with Napoli. [Aurelio] De Laurentiis is a great person and one of the best presidents I have ever seen.
"But the Neapolitans are not the only ones that are following Rodriguez. Let's see what the future holds. There are several European clubs after him, but it's best not to say anything at the moment.
"How much will he cost? I don't know. But what I can say is that his price has increased after the way he's played these past few months."
Napoli's third-placed finish in the Italian league last season means that they can offer Champions League football, although their 24-point gap to champions Juventus suggests that Rodriguez may struggle to win a league title with Napoli. The team certainly did not struggle for goals last season, but with Gonzalo Higuain being linked with a move to Barcelona, Rodriguez could potentially be a star for the Italian club.
Manchester United and Tottenham Hotspur
The Premier League duo have both emerged as potential suitors for Rodriguez over the last couple of weeks. After last season, Spurs could certainly use a player with the midfielder's talents, but last summer's post-Gareth Bale spending spree may put Rodriguez out of range this summer. Meanwhile, Man Utd are also rebuilding, and like Spurs have a new manager. Louis van Gaal's CV would surely catch Rodriguez's eye, but with the addition of Ander Herrera from Athletic Bilbao last week, Rodriguez may struggle to find a regular place in the side. Unlike the two Spanish sides, Napoli and Rodriguez's current club Monaco, neither United nor Tottenham will be able to offer him Champions League football next season. Given that he has excelled on the biggest stage in international football, Rodriguez will surely be looking to play in the biggest tournament in club football next season.
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Staying at Monaco?
Despite so many clubs supposedly chasing the Colombia international, it would not be the end of the world for him to remain with Monaco. The Ligue 1 side invested heavily in their squad last summer, including bringing in Rodriguez for a €45m (£35m) fee from Porto, and will presumably be stronger as a team now that they have a year's experience playing together. They missed out on the league title last season, but were just nine points behind champions Paris Saint-Germain and will feature in the Champions League this year. For Monaco to consider selling him after just a year, they would presumably be seeking to recoup their initial investment with interest, pricing all but the richest clubs out of the market, so it would not be a shock to see him remain at Monaco for at least another season. However, anything can happen in the transfer window, and there is still over two months before it closes.