Dundee United received two offers on Friday for striker David Goodwillie, neither of which was from Rangers, according to a Tannadice source.
However, neither offer matched United's £2m asking price for the 22-year-old.
A club spokesman told BBC Scotland: "No-one has met our valuation yet, but that doesn't stop people putting offers in. We've had two today. It's ongoing."
Cardiff City have discussed Goodwillie with United and it is believed they were one of Friday's bidders.
Rangers owner Craig Whyte told United they were asking too much for the striker.
"I think, for that individual player, £2m is too steep," said Whyte.
"But I am sure there are more conversations to be had with Dundee United."
The Bluebirds, who missed out on promotion to England's top flight via the play-offs, after the Scotland winger rejected a new contract with United and was also courted by Rangers.
Now new boss Malky Mackay has targeted Goodwillie, Scotland's young player of the year, as a component of his team for the forthcoming season.
Goodwillie was also United's top scorer last season with 18 goals and is under contract at Tannadice until 2013.
He received his first call-up for Scotland in November 2010 in a friendly against the Faroe Islands, coming on as a 76th-minute substitute.
Former Scotland winger Pat Nevin praised the player's ability to read the game.
Ex-Chelsea star Nevin, now a BBC football pundit, said: "Conway will be the appetiser, Goodwillie will be the main course.
"He is more match-intelligent than possibly generally any other home-grown player playing in Scotland just now.
"He really is a talent. He has a great eye for a goal. He'll always score goals and makes them himself as well. He's a very rounded player.
"There are one or two weaknesses to his game, which you always find with these very, very talented individuals.
"He's not fast - he's not lightening, however, he does make up for that with match-intelligence."
The Tayside club rejected two bids for Goodwillie in January because they did not match their asking price.
United manager Peter Houston is reluctant to lose his top scorer but would dearly love some extra funds to bolster his squad.
"I'm caught between a rock and a hard place with Goody," he told BBC Scotland.
"If he goes, it'll allow me to strengthen the team, but I'd be foolish to want rid of him. He scores between 15 and 20 goals a season.
"But we're a provincial club and, if somebody offers the right money for him, he'll be off.
"Rangers enquired about what his valuation was. The chairman told them what that is and I think Rangers felt it was a bit too much for them."