The Gers are keen on bringing the 28-year-old to Ibrox, and it appears that the Premier League side are willing to consider letting him leave the Amex Stadium next month as Sky Sports reports that the two clubs have held discussions about a potential deal.
It must be said however, that a move appears to be some way off being completed with Sky Sports suggesting that the Light Blues and the Seagulls are yet to agree a fee for former Scotland under-21 international.
It has been a frustrating season for Murphy, who made 35 appearances during Brighton's promotion-winning campaign in the Championship last season. This term, he has started just one Premier League game, while another three appearances have come from the bench for the former Motherwell man.
It may not be a surprise if it is not too long before there is a resolution to the talks now that Rangers do not play another competitive game until they travel to face Fraserburgh in the Scottish Cup on the 21st January.
Graeme Murty's men go into the winter break in Scotland on something of a high after their spirited performance against Celtic on Saturday saw the Gers come away from Parkhead with a 0-0 draw - with many feeling that they were the team that were more likely to bag the victory.