Sky Sports understands Derby goalkeeper Frank Fielding is having a medical at Bristol City.
The 25-year-old has made 80 appearances in total for the Rams and earned himself a call-up to Fabio Capello's England squad in 2010.
But with the signing of Lee Grant from Burnley, Derby boss Nigel Clough revealed he would allow the keeper to leave Pride Park in search of first-team football.
The Robins were understood to be interested in Fielding and this has moved on a stage as they bid for an immediate return to the Championship.
The 29-year-old, released by the Glovers at the end of the season, has agreed a two-year contract at Home Park.
Manager John Sheridan has also added Sean McCarthy and John Harbin to his backroom staff.
Former Argyle striker McCarthy returns to the club as first-team coach and veteran Australian coach Harbin has been named performance manager.
Sheridan told the club website: "I am very pleased to get my backroom staff sorted out.
"There is a lot of very valuable experience there - people who have played at the highest level and have coached at the highest level.
"We are now well set up to be able to get the best out of the players.
The appointment was expected after his previous club Queen of the South revealed on Monday he had agreed terms with the Ayrshire outfit to become their new boss.
Johnston will take his Palmerston assistant Sandy Clark with him to Rugby Park.
The 39-year-old - who spent five years at Killie during his playing career - replaces Kenny Shiels, who left the club by mutual agreement earlier this month.
A statement on the club's website read: "Kilmarnock Football Club is delighted to announce our new management team of Allan Johnston and Sandy Clark.
"The management, staff and players all wish Allan and Sandy the very best in their new positions and look forward to the forthcoming seasons."
Johnston emerged as one of the front runners to succeed Shiels after an impressive first season in management with Queens.
He led the Dumfries side to the Second Division title, as well as the Ramsden Cup - which included a victory over Rangers at Ibrox.
The new Kilmarnock boss will be officially unveiled at a press conference on Wednesday at 3pm.
