Swansea boss Garry Monk is adamant that only an “astronomical” bid could prise Wilfried Bony away from the club.
Everton manager Roberto Martinez hopes to complete the signing of midfielder Muhamed Besic in the near future.
The 26-year-old will sign the deal, which will keep him at Pride Park until 2016, when he returns from holiday.
Bryson, the club's player of the year in 2011/12, has scored 11 goals in 85 appearances since joining from Kilmarnock in the summer of 2011.
He told the club's official website: "I'm pleased to have reached an agreement to remain at Derby County for the next three years.
"I want to be part of what the club is trying to achieve, so it's great we've got something sorted and I've made it clear for a while that I've settled into the area and wanted to stay.
"I've really enjoyed the last two seasons and I think with the progress we've made in that time, especially in the last 12 months, we can kick on and make a real challenge towards the top six next season.
"We've got a strong team in place already with an excellent spirit and the manager has made no secret of the fact he wants to add to it over the summer to see if we can have an even better season next year, which is quite exciting."