HITC Sports understands that West Brom, Swansea, Newcastle and Crystal Palace are also keen on the Scotland international.
26-year-old Martin has been one of the finest strikers outside the Premier League since joining Derby in early 2013.
His two full seasons with The Rams have seen him hit the net more than 45 times and he has matured into a top target-man - and the interested clubs clearly feel his is now Premier League calibre.
Derby are keen to hold onto him, as he has two-years left on his current deal, but they know they cannot match any top-flight pay packet.
Newcastle are the latest club to join the hunt as Steve McClaren got the best out of him at Derby and clearly feels he could be a valuable addition at St James' Park.
However, former Toon boss Alan Pardew is a big fan, as is West Brom's Tony Pulis and Swansea's Garry Monk.
West Ham have also asked to be kept informed as they look to revamp their squad under Slaven Bilic.