City goalkeeping coach Steve Ogrizovic watched Murphy at Glanford Park on a couple of occasions but when Scunthorpe beat Tranmere to secure a play-off place and subsequently beat MK Dons and Millwall to get back into the Championship, things went quiet.
Murphy, who has played for the Republic Of Ireland is out of contract at the end of this month but has been offered a new deal.
It is understood that Murphy's wages are in keeping with Coventry's pay structure and that would not be a problem if City wished to sign him.