The 50-year-old was based at the Blues stadium while guiding Coventry to the Ligue 1 title and back to the championship.
Journalist Alan nixon says the Blues hierarchy has been impressed by Robins as they wait to hear from Slavisa Jokanovic and Chris Hughton.
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Lee Bowyer is also a candidate to replace Pep Clotet, while Nigel Clough has been linked, but BirminghamLive understands that will not go any further.
FC Groningen coach Danny Buijs has also been linked to a position that Clotet will leave at the end of the season.
Robins has led the Sky Blues to two promotions since his return for his second visit to the club. The former Manchester United striker also led Barnsley, Huddersfield and Scunthorpe.
This isn’t the first time Robins has been mentioned about Blues, with CEO Dave Boddy rejecting the possibility earlier this month.
Boddy said, “Mark and the football club remain committed to achieving our common goal of moving the club forward together.
“We have a very strong relationship with Birmingham City and they have been very good with us during our season in St. Andrews, so we are very grateful for that.”
“I spoke to Mark today and he joins the club in our common desire to move the club forward in the championship.”
Steven Gerrard was also linked to the position, but would have refused the Blues.