The Record states that Mark Warburton flew out to New York last week to discuss a potential move with the latter of the pair, while another report in the Record claimed that Barton was offered a three-year deal to join the Light Blues.
And Redknapp - who has managed the Croatian at three different clubs previously, while also being in charge for some of Barton's spell at Queens Park Rangers - suggested that if the Light Blues can get the two deals across the line, they would be great additions to Warburton's squad.
"Niko and Joey are very different players and very different characters, but both are very impressive in their own ways," he told the Record.
"As I have said, it goes without saying that both of them would be really excellent signings for Rangers for next season.
"Probably more importantly, it would certainly make the league up there very interesting having two players of that quality signing up for Rangers as they go back to the top league."
With the signings of Jordan Rossiter, Matt Crooks and Josh Windass already in the bag to bolster the Gers' squad, it appears that Warburton has now turned his attention to adding the kind of experience to his side that will perfectly complement the tremendous amount of youth within the first-team.
Both players have bags of knowledge from playing at the highest level so will be able to help the likes of Lee Wallace and Kenny Miller by passing that insight onto the other players in the squad.
And while Warburton may look at players like Barrie McKay as the ones that are going to help Rangers remain at the summit of the Scottish Premiership for several years to come, it will surely be the likes of Barton and Kranjcar that will lead them to the top in the first place.