Pitman has started the season on red hot form for the Cherries, netting a hat-trick on the weekend against Peterborough to open his account for the season following last campaign's tally of 28.
The Jersey product has scored 62 goals in a little over 110 starts since coming onto the scene in 2005.
It's unknown what sort of fee it would take to tempt Bournemouth into parting with their star striker, although it's expected that it would take at least a bid of £750k.
Premiership new boys Blackpool are also understood to be extremely interested in the 22 year old, along with the like of Doncaster, Watford, Ipswich and QPR.
Swansea have been on the lookout for a new forward since Brendan Rodgers arrived at the club last month and have been linked with Danny Graham, Tamas Priskin and most recently Leroy Lita.
This article first appeared on JACKARMY.net.