Lallana is playing in his second major tournament after featuring as part of the squad for the 2014 World Cup, but is enjoying his first spell on the main European international stage as a regular.
The 28-year-old started all three group games for the Three Lions as Roy Hodgson's side navigated their three opening fixtures without defeat, and has generally been one of the more impressive English stars in France.
The Liverpool man has continued his fine club form and has looked lively playing in an attacking midfield position, whether through the middle or from out wide, and has cemented his status as a regular in the side.
Redknapp is certainly an admirer of the former Southampton man and revealed that Lallana is perhaps the England star who has impressed him the most across the first three fixtures.
The former Liverpool and England star told Sky Sports: "I have been really impressed with Adam Lallana, he's been great, kept the ball well and looks like a really good international player. He just needs to add some goals and some assists."
Lallana will hope to keep his place in the starting XI as England now turn their attentions towards a last-16 knockout tie against as yet unknown opponents next Monday.
With almost a full week off, Hodgson has plenty of time to consider his team selection, and it is hard to imagine Lallana not featuring significantly in his plans.