Falcao is set to leave Old Trafford when his loan deal expires at the end of the season, before completing a move away from AS Monaco, either permanently or temporarily.
It’s understood that both Liverpool and Chelsea are keen to sign the Colombia international on loan, although the Premier League duo face competition from the likes of Juventus, Valencia and Inter Milan.
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Parker explains why Falcao should move elsewhere
But Parker believes Liverpool are simply not a big enough club for Falcao, who was widely regarded as one of the world’s best strikers prior to his ill-fated move to Old Trafford, while Chelsea are also not right for the South American ace because he would find himself behind Diego Costa in the pecking order at Stamford Bridge.
“There's just one problem: neither move makes any sense for the Colombian,” Parker wrote in his latest Eurosport blog. “In the position he is in, could he trust Jose Mourinho to give him a run in the team?
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“Not a chance. With Diego Costa there he wold be another Loic Remy, a bit-part player at best.
“As for Liverpool? Nice idea, but they are not quite big enough a club for Falcao; he must be looking for more than that. And being ex-United it's unlikely the fans would take to him – especially if he did not hit the ground running.
“It is great talk for Liverpool, though: even the suggestion that they can attract players of his quality shows that they are moving forward .
“To be frank, both moves are pipe-dreams. A move overseas beckons if he does not make the grade at United.”
Falcao is a shadow of his former self
In truth, neither Chelsea nor Liverpool should be considering moves for Falcao, who is now a shadow of the striker of scored goals for fun with Atletico Madrid and FC Porto.
The serious knee injury he suffered in January 2014 has clearly had a catastrophic affect on the Colombian, who has scored a disappointing four goals in 19 appearances for the Red Devils.
Although his motivation levels cannot be questioned, Falcao has looked slow and weak for almost the entire season, which makes the reported interest of Chelsea and Liverpool seem somewhat bizarre.
Still better than Balotelli?
Chelsea are looking for a striker to provide back-up for Costa, who played alongside Falcao at Atletico Madrid, with Didier Drogba expected to retire at the end of the season.
If Jose Mourinho truly feels Falcao still has plenty to offer then it will be interesting if he can get the best out of the forlorn forward, whose struggles at Old Trafford have reportedly reduced him to tears in recent months.
Falcao, however, might be an upgrade on Mario Balotelli at Liverpool.
The Italy international has scored a pitiful one goal in 13 Premier League appearances for the Merseyside outfit since joining the Reds from AC Milan last summer.
Should either Liverpool or Chelsea sign Radamel Falcao this summer? Have your say in the comments below!