Parker is expected to leave Craven Cottage imminently and take over at AFC Bournemouth following Fulham’s relegation to the Championship last season.
The former Blades boss was widely expected to take over at West Brom recently, but that didn’t materialise – which is understood to have led to Albion's sporting and technical director Luke Dowling leaving his role.
Dowling and the Baggies’ English-based board are understood to have wanted Wilder to succeed Sam Allardyce – but sources in the Midlands say that the appointment was vetoed by the club’s owner Guochuan Lai.
Aaron Ramsdale's classy message to Man Utd's Dean Henderson after Sheffield United goalkeeper is called up to England's Euros squad
And one insider with knowledge of the capital’s footballing scene has suggested Fulham will include Wilder’s name on a shortlist of candidates set to replace the former England midfielder.
Elsewhere at Bramall Lane, United could be forced to reconsider the structure of Arsenal’s proposed deal for Sander Berge – even if United officials are refusing to lower their £35m valuation of the Norway international.
Berge is expected to leave this summer, having expressed his desire to play in the Champions League again, and Mikel Arteta’s side are so far leading the race for the midfielder’s signature.
Sheffield United: Two of Slavisa Jokanovic's most trusted allies are set to join him at Bramall Lane
And although they will not lower their valuation of Berge, United may be tempted to soften their insistence that any deal is ‘front-loaded’ rather than spread over the duration of the Norwegian midfielder’s contract.
The Star also understands that United’s head of recruitment Paul Mitchell will continue his role when Slavisa Jokanovic takes official charge of the Blades next month.
Here’s a run-down of some other key transfer news from around the Championship…
9. Rams eye Mengi return
Wayne Rooney’s Derby County are expected to re-sign Teden Mengi on loan from Manchester United again this summer (The Athletic) Photo: Nathan Stirk
10. A blow for the Blues
Birmingham City have failed to agree terms with Alen Halilovic over a new contract, with the Blues now looking to bring in another attacking midfielder as his replacement. (We are Birmingham) Photo: Tony Marshall
11. A clean Slate
Hull City and Preston North End are keen on Sheffield United midfielder Regan Slater, who saw the Blades extend his contract by another 12 months recently Photo: Jacques Feeney
12. Boro face competition for Bolasie
Middlesbrough want to re-sign former loanee Yannick Bolasie from Everton – but face strong competition from rival Championship clubs who can offer more lucrative terms for the winger (TeesideLive) Photo: Ross Kinnaird