St Johnstone are one of a number of clubs trying to sign young Hibs striker on a season-long loan.
Saints boss Tommy Wright is on the hunt for a new forward and has been foiled in his attempts at signing Stevie May from Aberdeen, while another one of his targets in Kane Hemmings opted for Dundee rather than McDiarmid Park.
The Perth side, however, face competition for Shaw, with a clutch of other teams in the Scottish Premiership also keen to land the 20-year-old on loan.
Shaw has been an unused sub in the Easter Road side's first two Ladbrokes Premiership games. He played last week for Hibs Colts in the Tunnock's Caramel Wafer Challenge Cup, scoring in 4-3 defeat by Elgin City.
Although Shaw is rated highly by Hibs, the club may allow the player to get more first-team experience as the Scotland Under-21 forward is currently behind summer signing Christian Doidge and Swiss hitman Florian Kamberi in the pecking order.
Shaw played 26 times in the league for Hibs last season, scoring six goals.