The West Ham manager believes the striker, who netted a treble against Arsenal this weekend, can bring a unique skill set to the Three Lions squad.
Though he has suffered one or two minor problems, Carroll has largely been fit since making his first appearance of the season in mid-September after returning from a long-term problem originally suffered in February 2015.
Having already scored four important goals for the Hammers earlier in the campaign, the 27-year-old put in his best performance in recent memory to score a quickfire hat-trick against Arsenal in Saturday's 3-3 draw at Upton Park.
With Carroll's chances of featuring for England this summer virtually universally written off, Bilic claimed that the striker's latest performance has given Roy Hodgson food for thought and stressed his belief that the striker possess unique qualities that would make him a huge assest for the Three Lions.
Bilic told reporters, as quoted by Eurosport: "I've said my opinion about a few of our players. Mark Noble, Aaron Cresswell.
"Andy Carroll is definitely in the category that he has to make you think about him because there are not many players capable of doing what he is doing. But it's Roy's decision.
"His problem is not consistency in terms of little injuries. A lad who is six foot whatever and with so many kilos - he needs to be fit. Now he is fit we hope he is going to last like this for years."
If Carroll could build on his success and build up a head of steam in the remaining weeks of the season, he may stand an outside chance of being named in Hodgson's squad for the tournament in France and being handed a first England cap since October 2012 in the final warm-up matches after the end of the domestic season.
Hodgson named Harry Kane, Jamie Vardy, Danny Welbeck, Daniel Sturridge, and Theo Walcott as his attackers for last month's friendlies against Germany and the Netherlands, but that selection is arguably missing a player with the raw power and strength of Carroll.
The former Newcastle United and Liverpool man will be hoping to retain his place in Bilic's side when the Hammers host Manchester United in their FA Cup quarter-final replay against Manchester United at Upton Park on Wednesday night.