Mee and James Tarkowski have formed a successful union at the heart of the Clarets’ defence and are repeatedly championed by their manager for international recognition.
While Tarkowski has been capped twice by Gareth Southgate, Mee has only represented England at age-group level and, having recently turned 30, time is running out for the centre-back.
Dyche said: “Ben eventually could become Steve Bruce. It’s well-documented about Steve Bruce never playing for England and Ben Mee could become one of them, and might well do.”
Both Tarkowski and Mee were overlooked by Southgate in his squad for the Euro 2020 qualifying trips to the Czech Republic and Bulgaria as 21-year-old Chelsea defender Fikayo Tomori was given his maiden call-up.
Dyche continued: “For (Tarkowski) and Ben, they both scratch their heads. I definitely think either or both should be considered at very close quarters to be in the England set-up, at least.
“Tarky’s slightly different; he’s a bit younger and been in the England team before.
“But it’s not an easy job as an international manager and I’ve always thought Gareth’s trying to look for now and keep interest in the future by getting players in early.
“If you look at (Aston Villa defender Tyrone) Mings and Tomori, very little experience which is probably the biggest surprise, but I understand trying to blood them early and get them in the system early.
“I haven’t spoken to Gareth, they’re just my thoughts from the outside looking in.”
Nick Pope retains his place as one of three goalkeepers, alongside Everton’s Jordan Pickford and Aston Villa’s former Burnley custodian Tom Heaton.
Dyche believes it is a sign of Burnley’s progress since he took charge in 2012 that his players are either being named in England squads or touted for call-ups.
He added: “It’s interesting for me. Over these years and now we’re very confidently talking about Burnley players being in the England team.
“I remember when Tom Heaton got his first call-up. It was like ‘wow, Burnley have an England player, they haven’t had one for however many years’ and now we’re talking about it free and easy.
“It’s good to say that Burnley players are being talked about as freely as we are talking about them with the national side.
“The players keep active, they keep at it, they keep working hard and who knows what the future will bring?”