That leaves them in limbo about including the fullback on their Super 15 roster with the cutoff date for that list to be filed with the NZRU later this month.
"With a lot of young players we need someone to be the glue and someone like Mils would be ideal," coach John Kirwan told the Blues website.
He was extremely interested in hiring Muliaina who played 49 games for the Blues before transferring to the Chiefs for a further 41 matches.
Muliaina would be an ideal signing to play centre for the Blues where his leadership would help many of the younger players in the backline.
The Chiefs have also been hunting Muliaina's signature.
Kirwan has the view that if he returns to the Super 15, he will do what is best for him and his family.
It is understood the Super 15 teams have made a mix of offers to NTT Docomo asking that Muliaina gain a release, play for them on a sabbatical system or stay with the club.
Kirwan is still waiting for an answer from Ma'a Nonu about his Super 15 employment next season.
The All Blacks and Blues second five-eighths was supposed to signal his 2013 intentions by now but he was granted an extension because of his test commitments.
The NZRU agreed to that concept so the Blues and Highlanders must wait to see if Nonu chooses to be part of their group next season or brushes both and heads offshore.
"The way he is playing he looks very settled," said Kirwan. "I don't know which way that is but I hope I am reading that body language the way I would like it. I have no issues with him waiting until he gets past these tests."
The Blues are still seeking some tight forwards and Jamie Mackintosh is one of those targets once loosehead prop Tony Woodcock decided he was switching from the Blues to the Highlanders.
The squad's senior locks Ali Williams and Anthony Boric are both tracking well in their recovery from injury with Williams to return to ITM Cup action for Auckland tomorrow against North Harbour.
Boric is some way short of playing after neck surgery but is reported to be making a strong recovery in the gym.
Meanwhile, there is a market buzz that delisted five-eighths Gareth Anscombe is negotiating with the Chiefs to be part of their next squad.