Chelsea chairman Bruce Buck has said the club are unsure if they will bid again for Tottenham's Luka Modric.
Manager Andre Villas-Boas has admitted he is short on midfielders and there was little thrust from that department in the 0-0 draw with Stoke on Sunday.
But having had one reported offer of £27m rebuffed by Spurs, there are doubts Chelsea will increase it before the transfer window shuts on 31 August.
"Spurs rejected our offer and I don't know if it will go further," said Buck.
"Andre didn't give us a shopping list but he did tell us where he thought we could improve.
"He did mention some players but it was not a case of 'I want this guy and I want that guy' because it is more than just selecting the players.
"It is whether the player is available, what the price is and every other dynamic that goes with it.
"But Andre is working very well with the board and directly with [owner] Roman Abramovich in terms of looking at the squad and trying to see whether there is anything that needs to be done."
Tottenham are adamant they will not sell Modric, 25.
Before the goalless draw at the Britannia Stadium on Sunday, Villas-Boas said: "We play 4-3-3, we have a squad of 25. For you to prepare for a game, you need at least six midfielders. We only have four."
With Michael Essien out with a knee injury, the Portuguese picked John Obi Mikel, Ramires and Frank Lampard to start the game against Stoke, with Yossi Benayoun coming off the bench.
Villas-Boas's other midfield options include 18-year-old Josh McEachran, who was an unused substitute.