The Colombia international has been heavily linked with a move to Old Trafford in the summer transfer window after being frozen out at Real Madrid under Zinedine Zidane.
Indeed, Zidane didn’t even include the South American playmaker in his Real Madrid squad for last weekend’s Champions League final.
Rodriguez only started 13 games in Real Madrid’s title-winning campaign after falling behind Gareth Bale and Isco in the pecking order at The Bernabeu.
The former Monaco star has been linked with Chelsea, Liverpool and Manchester United since the Premier League season finished.
Manchester United has proven the most persistent link as Jose Mourinho looks to improve his squad ahead of a return to the Champions League.
However, former Liverpool midfielder Hamann has warned Manchester United not to sign the Real Madrid midfielder because he believes him to be out of shape.
“Manchester United shouldn’t go anywhere near James Rodriguez!” Hamann wrote in his Paddy Power blog.
“He always looks overweight and United already have enough flaky players who go missing in tough situations, so I’d steer clear.”
Manchester United secured their place in the Champions League next term thanks to a 2-0 win against Ajax in the Europa League final.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news