Leicester have tabled an offer of £30million for Tarkowski, but Dyche indicated the 27-year-old was central to his plans.
“It will be a board decision. I certainly want to keep him, make no mistake,” Dyche said.
“He is a very important player here and I feel it is very important that we keep him.”
It will be a board decision. I certainly want to keep him, make no mistake
Tarkowski is yet to feature for Burnley this season citing injury. A toe problem was not thought to be serious but has now ruled him out of the opening four games of the season.
“He’s got a sore toe, so we’re having to wait for that,” Dyche said.
“He said to me it’s not serious, but it is sore, that’s the way that one is.
“He’s had all the checks, everything has been done.”
Tarkowski was one of seven first-team players missing for Saturday evening’s 1-0 home defeat to Southampton, leaving Dyche battling the same player shortages he faced at the end of last season after the likes of Jeff Hendrick, Aaron Lennon and Joe Hart left when their contracts expired in June.
Dale Stephens is the only major signing of the summer so far, and the ex-Brighton man was pressed into an immediate debut after his arrival on Thursday.
“I thought in the second half he got stronger,” Dyche said. “The first half was a bit quick, he was getting his eye in, getting his body going. He knows the Premier League but he’s not trained much.
“I threw him in slightly out of necessity. He is a good player but we’d ideally hold players back for a week’s training so they can get a feel for what we do.
“I’ve asked him to do a shift and he’s done that and the second half was a good performance.”
With two more games this week – including a Wednesday night meeting with Manchester City in the Carabao Cup – Dyche does not expect his injury woes to ease soon.
“I’d be very surprised,” he said. “(Ashley) Barnes might have a chance. It would be good to welcome him back but obviously we’ve got be careful with so many injuries. Every game is important.
“We don’t want to risk players and have them out for an even longer period. The international window will hopefully be a useful period to get them closer to fitness.”
Victory for Southampton gave Ralph Hasenhuttl’s side their first points of the campaign, and came thanks to a far more robust defensive showing than in last weekend’s 5-2 loss to Tottenham.
“It was clear what we have to expect at this ground, it is very tough work against this opponent, but I think we showed what we have worked on during the week,” Hasenhuttl said.
“We were much better organised, more disciplined and hard defending. It was a good step forward.”
