He is out of favour at Tynecastle Park and, although Hearts wanted him to stay, he has chosen to move in the hope of more regular first-team football.
Adams is a huge admirer of the 28-year-old and will give him creative licence within the Bradford side, believing he can help open opposition defences.
He is expected to challenge for a starting place each week after spending most of the season on the bench or in the stand in Edinburgh.
After signing Dion Pereira from Luton Town last week, Adams is preparing to tie up his second signing of the January transfer window. He hopes to complete the deal for Walker before the week is out.
“We’ve added Pereira and we will probably add before the weekend,” Adams told the Bradford Telegraph and Argus.
“We have a strong position just now with signing a player. We’re hopeful we can get it over the line before the weekend.
“We’ve been looking for a player of his type that can get at defenders, take the ball for a run and find that through pass that our strikers can take.”
Walker was due to undergo a medical and complete paperwork before the move can be formally announced by the clubs.