The 23-year-old has gone from strength to strength since swapping Sporting Lisbon for Tottenham, being converted from a centre-back to a defensive midfielder by Mauricio Pochettino and establishing himself in the England setup.
However, an 18-month loan spell at Goodison Park nearly saw Dier move to the Premier League on a permanent basis two years before his switch to White Hart Lane, having impressed in the academy.
"We wanted to sign Eric and, at one point, thought we were going to get him," Stubbs told the Liverpool Echo.
"It took us the best part of eight months to get him up to speed but you could see his game coming on 10-fold and that was when we decided we wanted to sign him and we were in negotiations to do it but, at the time, it was going upwards of £1m, which wasn’t where Everton were at the time.
"Now they wouldn’t blink at two, three or four million for him, so for Eric at that time it would’ve been a case of right place, wrong time."
Dier, who eventually joined Spurs for a little over four times what Everton was quoted, had spent his entire footballing career in Portugal before the move - his family having emigrated when he was seven years old - and Stubbs admits the versatile midfielder had problems adapting to English football.
He said: "When he came, he was way off the pace because he had come from a really different culture. He was brought up in London but had gone over to Portugal and was with Sporting and you could see that he was used to that slow tempo of football whereas here it was fast, frenetic and he struggled fitness-wise to start off.
“Everything was happening too quick for him. He was getting closed down on the ball and we knew he had ability and was comfortable on the ball, had a languid style but was very quick once he got going into his stride.