Olsson left Norwich on Tuesday and could be replaced by Bradford's Australia international, while Rowett is reportedly keeping an eye on Alex Neil's job.
Olsson was sold to Swansea City in a reported £4 million deal on Tuesday, leaving Norwich on the lookout for reinforcements in the Swede's position.
Meredith, who has helped Bradford to fourth in League One this season, is out of contract at Valley Parade in the summer.
Bradford City's James Meredith (left)
Bradford are said to be desperate to tie down the twice-capped Australia international, however it is claimed Norwich could test the Bantams' patience with an immediate approach.
The former Derby County player would likely jump at the chance to move up a division, though given a straight choice, he may look to remain in Yorkshire with Leeds, having spent the past eight years in the county with York City and Bradford.
Ex-Birmingham boss Gary Rowett
Meanwhile, the Mirror reports that sacked Birmingham City boss Gary Rowett is keeping an eye on the managerial situations at both Norwich and Bristol City, having snubbed a chance to take the reins at Nottingham Forest.
Would Meredith be a good signing for Norwich?
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