Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
Liverpool manager Brendan Rodgers is keen to add at least two more players to his squad as he continues to strengthen for the new campaign.
His first four signings - Kolo Toure, Iago Aspas, Luis Alberto and Simon Mignolet - joined up with their new team-mates for the first day of pre-season yesterday.
But with midfielder Jonjo Shelvey on the verge of a move to Swansea after a £6million fee was agreed the Reds boss is continuing to assess his options and he is still looking to bring in another forward and a defender.
"I still think another attacking, creative player, and depending on what goes out of the club - because naturally there might be one or two players who need to go out and play more - then we'll need to fill those areas that have been vacated," he said.
"Certainly another attacking player will really benefit us, and probably another defender.
"We'll see how it develops over the course of the next few months."
The club remain interested in Shakhtar Donetsk's attacking midfielder Henrikh Mkhitaryan but the deal is a complicated one, although not as byzantine as some are suggesting.
Press Association Sport understands Liverpool are unaware of any reported third-party ownership issues.
They were led to believe if they met a clause in Mkhitaryan's contract, understood to be in the region of £20million and a price the Reds are willing to pay, the deal could progress.
However, the Ukrainian club continue to change the terms and with money not an issue - they are backed by billionaire Rinat Akhmetov, listed the 47th richest man in the world in March - they have no incentive to sell.
Rodgers is considering his options in terms of another centre-back after deciding Schalke's £19million valuation of Kyriakos Papadopoulos, who missed most of last season with a knee injury, is over-the-odds.
However, it seems even though he has money at his disposal the manager will not spend just for the sake of it if he cannot secure his priority targets.
But the future of Luis Suarez, who has spent much of the last month seemingly publicly courting Real Madrid after expressing his unhappiness with the British media, may necessitate a change of approach.
Shelvey's departure would go some way to balancing the books on the back of the departure to West Ham of striker Andy Carroll for a deal potentially worth £19million.
The purchases of Celta Vigo's Iago Aspas, Sevilla's Alberto and Sunderland's Mignolet - Manchester City defender Kolo Toure was a free transfer - has amounted to about £23million.
Other players likely to exit Anfield this summer include midfielder Jay Spearing, who spent last season on loan at Bolton, and Uruguay centre-back Sebastian Coates although there has been little interest in them so far.
When Rodgers took over in early June last year he was not able to fully benefit from the transfer window and errors were made late on which saw Carroll loaned to West Ham the day before the August deadline and a deal for Clint Dempsey fall through at the last minute.
Getting the majority of his business done early this time around was key for the Northern Irishman.
"It's great - it's a big thing to the club because we looked at last summer and there were lots of things that were difficult for us," he told liverpoolfc.com.
"That meant that the opening period of the season was difficult.
"From that we've got all our people involved, our recruitment team in - and they got to work as soon as they came in.
"We brought great signings (Daniel Sturridge and Philippe Coutinho) in in January and that's really helped us.
"Obviously the plan was to get our signings in as soon as we possibly could - and we still hope to make a few more.
"I'm very happy with the four players I've brought in, and they'll add to the group."