The 23-year-old recently told Laudrup that he would not sign a new deal at the Liberty Stadium, and with less than a year to run on his current deal he was widely expected to leave before the transfer window closes on Friday.
City were understood to have made an initial bid of around ?5million, but Swansea were keen for a higher offer as Chelsea will get a percentage of any fee due to a sell-on clause inserted when Sinclair moved to south Wales in 2010.
City returned with an improved offer, but it is understood it was turned down by the Swans - who are determined to have their valuation of the player met.
Laudrup would not confirm or deny that an offer had been rejected following his side's 3-1 Capital One Cup win over Barnsley, but admits the deal could still happen.
He said: "I can't say, I really don't know where we are at the moment.
"Even if talks have broken down there is still time for everything to happen, I am not saying he will go, or he will stay.
"The point where we are now could change completely.
"From a manager's point of view, Scott is an important player and he plays in a position where we don't have that many players and if he leaves we need another one.
"That's the balancing act and the closer we get to the deadline the more difficult and shaky it will be."
Laudrup is keen to bring in targets Pablo Hernandez and Marvin Emnes from Valencia and Middlesbrough respectively and the Dane expects there to be plenty of activity over the next few days.
"I think it will be very busy," he said. "Everyone here will have to be working hard over the next three days to make sure we are not in a situation where a club is saying 'the fax is not working'. I tried that, where a fax wasn't working in a club and they signed a player a little too late.
"Luckily I think we have two or three fax machines here."
Laudrup was speaking after watching his side maintain their 100% start to the season by beating Barnsley, with Luke Moore weighing in with a double.
Danny Graham also got on the scoresheet, although the top-flight side had to survive some nervous moments when Bobby Hassell pulled it back to 2-1, before Moore settled matters with his second.
And Laudrup, who handed debuts to record signing Ki Sung-yueng and Kyle Bartley, admitted he had not been happy with elements of the Swans' performance.
He said: "I am always satisfied when we win.
"But I was not happy with the first 25 minutes and neither were the players.
"We did not have the ball, we missed a lot of passes and defended with two deep lines.
"But we were much better in the last 20 minutes of the first half and we had more possibilities and the tempo of our play was higher and we got the opening goal.
"I was pleased with the second half, there were moments after it went to 2-1 where we struggled for six or seven minutes, but more or less I was pleased with what I saw in the second half."
Barnsley boss Keith Hill commended his side's display as they responded with a battling performance following their 5-1 drubbing against Brighton at the weekend.
He said: "I am encouraged, after Saturday I felt I had been dealt a low blow to the groin area. We needed to take tiny steps tonight and we got them.
"But at the minute, like last season, we are guilty of shooting ourselves in the foot with the individual errors we are making.
"The three goals were avoidable tonight, but we can take a lot of encouragement."
