The Millers are keen on bringing the Birmingham midfielder to the AESSEAL New York Stadium, but boss Neil Redfearn revealed at the weekend that they are in a chain which is stuck further up.
Ramirez's move to promotion-hopefuls from Southampton could now have a domino affect as his arrival is likely to see Blues target Fabio Fabbrini return to parent club Watford, allowing him to move to St Andrews on a permanent deal.
Only then will Gary Rowett allow Shinnie to move to South Yorkshire.
As well as Shinnie, boss Redfearn is hopeful of bringing at least one more body in before the January window slams shut next Monday.
He said: "There's maybe one other. We've got to concentrate on what we
can do and hopefully we can get it done."
Redfearn's in-tray has suddenly become more occupied over the last couple of days as he continues his search for a new assistant manager and he awaits news on whether on-loan midfielder Grant Ward's stay from Spurs is going to be extended until the end of the season.
Redfearn was of the understanding that an agreement was in place for after Ward's final game on Saturday, but the midfielder himself cast doubt on that, saying he had heard conflicting reports.
One thing that is for sure, though, is Redfearn's admiration of the 21-year-old who impressed again during the 2-2 draw at Cardiff on Saturday.
"I thought our standout player was Grant Ward. He was
outstanding from the first minute to the last.
"You've got to remember this
lad's tender age. He's come on in leaps and bounds. I think you can play Grant
anywhere in midfield.
"He's got that sort of ability. He's one of these who
deals with the ball in tight situations. He's got a turn of pace to get away
from people, as all top-class players have.
"I think he's growing into this
level of football, which is a tough level for young players. He's developing
unbelievably."
