After selling Harry Maguire to Manchester United, Leicester turned to Tarkowski, while Wolves were also linked with the 26-year-old, but Burnley stood firm.
Clarets boss Sean Dyche praised Tarkowski for his performance in last weekend’s 3-0 victory over Southampton, and Mee has been impressed by his centre-back partner’s reaction.
“You never know what can happen,” said Mee. “Obviously there was a lot of talk around Tarky. I’ve said to him, ‘I’m glad you’ve stayed.’ He focused really well and he showed that on Saturday.
“He had the attitude of what will be, will be. He never once stepped out of line. You see other players at other clubs, you hear about something and they can go a bit off the rails. He’s stuck to it and trained really well and stuck with the group. He’s fully focused on playing for us.”
Tarkowski stepped into Michael Keane’s boots when he left Turf Moor for Everton two years ago and has formed a strong partnership with Mee.
Both men were mentioned as possible England internationals during Burnley’s brilliant season in 2017-18, when they finished seventh, with Tarkowski winning two caps.
“We’ve done well over the last couple of seasons and hopefully long may that continue and he can be here and we can build the partnership even stronger,” said Mee.
Tarkowski was put on standby for the World Cup in Russia but pulled out to have a hernia operation. He then needed surgery for a second time last November, sitting out a month of the season, and has been out of the England picture since.
But England boss Gareth Southgate has been a regular visitor to Turf Moor over the past two seasons and, with goalkeeper Nick Pope now fit and first choice again, Tarkowski will hope to catch the eye.
“I hope they can look at him and see what he can do and he can get back in there,” said Mee.
“I know he was disappointed not to be in and around it the last couple of times. A few good performances and I’m sure he will (get back in).”
Burnley struggled last season after beginning their campaign early in the Europa League but they showed the benefits of a full pre-season with a fine opening performance against Saints.
They will try to end a run of eight successive defeats against Arsenal when they travel to the Emirates on Saturday, with games against Wolves and Liverpool also to come before the first international break.
“It’s only one game in but we’re determined to show everyone what we can do and how much we do deserve to be in this league,” said Mee, who was given the captain’s armband on a permanent basis following the departure of Tom Heaton.
“We want to better last year, obviously, and be more consistent in our season. If we have the same sort of year as we did the back end of last season, we’ll have a good season.”