David Moyes faces a frantic last day of the transfer window after an unconvincing display from Manchester United's midfield reinforced the need for a major signing before the 11pm deadline.

Athletic Bilbao's Ander Herrera and Everton's Marouane Fellaini and Leighton Baines are targets but Moyes may have to return to their respective clubs with a final, deal-making offer.

Daniel Sturridge's goal at Anfield consigned Moyes's side to a league start of four points from three games. Yet the Scot claimed that on the basis of what he described as United's "best performance" so far, he would not be concerned if no additions were brought in before Monday's deadline. The manager has had a €30m (£25.5m) offer for Herrera and a £36m joint bid for Fellaini and Baines rejected while he has also inquired about Roma's Daniele De Rossi.

"We will continue working for what's left of [the window] to try and get what we can in," said Moyes. "I've got to say I was really impressed with how the players played today. I tell you what Ican see why they're champions. So as far as transfers go we've only got I don't know how many hours left but not too long to wait."

Moyes said he would not be concerned if he bought no one before the window's closure. "Well, not [on] today. I thought they played really well," he said. "They dominated [the] game for long periods without us maybe having the final bit, the final pass, cross at different times." The Scot would not be drawn on how confident he is of strengthening. "I couldn't give you a heads-up one way of the other at the moment," he said.

The Bilbao coach, Ernesto Valverde, left Herrera out of the side that lost 3-1 to Real Madrid but said he does not expect the midfielder to move. If United meet Herrera's €36m buy-out clause, Athletic will be unable to prevent his departure, so long as the player wants to leave. Valverde said: "He is a very important player for us. My decision today [to put him on the bench] had nothing to do with the offer."

While Baines and Fellaini are reportedly keen to join United, even a bid of £40m or more for both may not be enough. Everton are thought to be more minded to allow only Fellaini to depart. They are lining up Wigan's James McCarthy in anticipation of Fellaini's departure but the Championship club's chairman, Dave Whelan, said he had turned down an offer from Everton. "We rejected the bid because it's still not near the value we'd expect," he said.

Chelsea's Victor Moses, Paris Saint-Germain's Mamadou Sakho and Tiago Ilori of Sporting Lisbon were at Anfield to see the win over United and Brendan Rodgers, the Liverpool manager, hopes to complete their respective deals on Monday. The defenders Sakho and Ilori should join for a combined fee of around £25m while Moses should arrive on a season-long loan from Stamford Bridge.

"We hope they can be completed later but there will be no confirmation until tomorrow," said Rodgers, who may also sign the Aston Villa goalkeeper Shay Given as cover for Simon Mignolet. The striker Fabio Borini may go out on loan to Sunderland or Queens Park Rangers.