The 23-year-old has scored a remarkable 33 goals in 50 league appearances at Rovers, where he has continued the prolific form in front of goal which he showed at Huddersfield prior to his B£8million move to east Lancashire in 2012.
Rhodes was strongly linked with a move to Sky Bet Championship rivals Wigan towards the end of August although Blackburn boss Gary Bowyer always maintained the Scotland international would remain at Ewood Park.
Latics' coffers were substantially boosted by the sale of midfielder James McCarthy to Everton in the final throws of the August transfer window and, with that cash injection, chairman Dave Whelan may consider testing Blackburn's resolve again in January.
However, Shaw is adamant the club's owners, the Venky's, are keen to keep hold of their prized asset.
Speaking to Press Association Sport about rumours linking Rhodes with a switch to the DW Stadium last month, Shaw said: "There was a lot of talk in the media but there wasn't a lot of talk here.
"We stated that Jordan wasn't for sale and the owners don't want to sell Jordan Rhodes.
"It's the owners' ambition, the fans' ambition and the club's ambition to get back to the Premier League and you don't want to sell your best players, you don't want to sell Jordan."
- Sports & Recreation
- Jordan Rhodes