Sky Sports sources understand Rangers have made a formal offer for Dundee United striker David Goodwillie and increased their bid for Hearts defender Lee Wallace.
United claimed earlier this week that Rangers had failed to follow up their initial enquiry for Goodwillie with a firm bid.
However, Rangers have now firmed up their interest with a formal bid as they look to win the race for Goodwillie's signature.
United are resigned to losing the Scotland international with Cardiff City also expressing an interest in the highly-rated 22-year-old.
Rangers are hoping to make it a double signing by agreeing a deal for Hearts full-back Wallace.
The Scottish champions have already seen one bid rejected for Wallace, but they are now thought to have come back with an improved offer in the region of £1million as they look to persuade Hearts to do business for the Scotland international.