Last season, Murphy played a key role as Brighton secured promotion to the Premier League, with the 28-year-old making 40 appearances in the second tier.
However, Murphy has featured for just 166 minutes in the top flight this season, with the wideman's last appearance coming on September 24.
According to Sky Sports News, Murphy's lack of action at the Amex Stadium has led to Rangers showing an interest ahead of the January window.
The Glasgow giants are looking for reinforcements to try to boost their chances of finishing in at least second spot in the Scottish Premiership, and Murphy could potentially be tempted into a return to north of the border.
Murphy spent the first six years of his career at Motherwell before deciding to join Sheffield United in 2013.