The 27-year-old featured in the Championship Playoff final at Wembley where Derby County narrowly missed out on promotion at the hands of Queens Park Rangers, who clinched victory with a late goal from Bobby Zamora.
Bryson signed for Derby for around £450,000 from Kilmarnock in the summer of 2011, and has since gone on to make 130 appearances for the Rams scoring 27 league goals.
The Scotland international has established himself as one of the top players in the division during his time in the Championship, and was this season declared Derby County's Player of the Year as well as making it into the official PFA Championship Team of the Season.
At the age of 27 Bryson is arguably at the peak of his career, and will no doubt be keen to test himself in England's top flight while time is on his side.
There is yet to be any report regarding the proposed fee offered to Derby by QPR, but news last week suggested that the Rams had turned down an offer in the region of £750,000 for the midfielder's services from Burnley.
Derby also stated that the club were in ongoing contract negotiations with their star man and were looking to tie up a deal to secure Bryson's future.
Redknapp is keen on strengthening his midfield options at Loftus Road this season, and after Steve Sidwell opted for a move to Stoke rather than join QPR, Bryson may well be the next target on the 67-year-old's shopping list.