Falcao scored just four goals during his season-long loan at Old Trafford in 2014/15, finding himself in and out of the side, and a few eyebrows were raised when Jose Mourinho took the opportunity to take the Colombian on loan for a season from Monaco this summer.
Souness may have touched on a couple of reasons why Falcao didn't live up to expectations at United, including an ACL injury he had only just recovered from, and the lack of regular game time.
The Scot said: "He goes to Manchester United and was finding his feet after an ACL injury. That's the injury players don't want because there's no guarantee you'll come back the same player.
"No matter how good Falcao was before that injury, that would have been in his head.
"He went to Man United, who were chopping and changing their team at the start of last season, looking for a formula. He was in and out of the team and never really got a run of games and I just think he's (now) gone to a team that's settled.
"The system is settled and players are playing with confidence. They're the current champions."
Of course, returning to action from a serious injury in a different league with a club that has so much expectation when it comes to performing is not going to be an easy environment to succeed in.
The same kind of expectation won't be on Falcao's shoulders this season at Stamford Bridge, as Diego Costa is Jose Mourinho's first choice forward. But with his injury record over the past year, Falcao is more than likely to get his chance, and there are plenty more opportunities for him to make an impression this season, but he may still lack the rhythm that is required in order for him to find some good form.
It will be a tough ask for Falcao to find the kind of form he showed at both Atletico Madrid and Porto, which made him one of the hottest properties in Europe, but even a fraction of that could prove to be a useful asset for the Blues this season.