The Terriers made a move for the former Manchester United striker on Monday night as they seek a replacement for the sacked Simon Grayson but saw that request initially rejected.
The Sky Blues have now given their manager permission to talk to the npower Championship club.
A statement read on the Huddersfield website: "Huddersfield Town can confirm it has reached an agreement with Coventry City, who have granted permission for the club to speak to Mark Robins.
"Talks will commence immediately."
Robins has only been in charge at the Ricoh Arena for 33 games but has led the Sky Blues on a superb revival and they are in play-off contention in npower League One.