The 22-year-old had a spell on trial with Rovers last week and he has been invited back by Hughes, who wants to take a second look at the player.
However, the South African international, who plays for the Swedish side Djurgardens, is also expected to spend several days at Newcastle this week.
"Things went very well at Blackburn and Mark Hughes has already asked me to return for a few days," said Davids. "I will now be at Newcastle for a few days and hopefully I can make a good impression there as well.
"I feel that, at this stage of my career, I would like to move to a bigger club and Djurgardens know this.
"I have their full backing, although they would like to keep me for at least another season."