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Liverpool FC's search for a new striker rumbles on after it emerged their hopes of signing Radamel Falcao have been dashed.

But the Reds are in the hunt Uruguayan hit-man Edinson Cavani, according to the player’s agent, who says they have made an approach for the Paris Saint Germain forward along with Arsenal.

Liverpool are understood to have made tentative enquiries about the availability of taking Falcao on loan this season but the club have been told that if the 28-year-old is to leave Monaco then it will be for Real Madrid.

A season-long loan fee could have cost the Reds as much as £12m and Colombian striker Falcao would have also demanded a huge salary, with some reports suggesting he earns £10m a year, tax free, playing in the principality.

And it is believed that Falcao favours a return to La Liga where he flourished at Atletico Madrid and earned his big money move to Monaco last summer – but now he wants to play for their city rivals Real.

Liverpool will keep tabs on his progress but are increasingly resigned to missing out on the South American striker.

Cavani, meanwhile, is said to be interested in a move to the Premier League and his representative claims Liverpool and Arsenal have made an approach.

It remains unclear whether the 27-year-old is on Liverpool manager Brendan Rodgers’ list or not but Cavani’s agent, Claudi Anelluci, insists the Reds have enquired about his transfer.

“There has been much interest in the player during the last six months,” Claudi Anelluci is quoted in El Telegrafo as saying.

“I can confirm that Cavani heard proposals from Liverpool and Arsenal.

“(Cavani) Already said he would love to play in England, but has not yet made a final decision.

“He is not interested in money and fame; he just wants to be happy playing football.”

Liverpool have been looking to fill the void left by Luis Suarez ever since he was sold to Barcelona for £75m earlier this summer.

Rodgers, who has already brought in Rickie Lambert from Southampton for £4m, looked to have sealed a deal for Queens Park Rangers’ Loic Remy.

However, with the transfer close to being finalised, Liverpool pulled the plug following complications over his medical.

The Reds open their Premier League account a week on Sunday against Southampton and to compound their striking woes, Daniel Sturridge left their tour of the US early after picking up a hamstring injury.

Rodgers insists the England striker will be fit in time for the season’s opener, however.

It remains unlikely that Sturridge will be paired with Swansea City’s Wilfried Bony, despite constant speculation linking Liverpool with a move.

The Ivory Coast international was on a list of potential replacements for Suarez but the Reds are understood to have cooled their interest.

Bony’s buy-out-clause is believed to be £19m and his wage demands are likely to have put Liverpool off.

The future of defender Daniel Agger, meanwhile, remains uncertain. Croatian defender Dejan Lovren was signed from Southampton for £20m last week and his arrival is certain to see Agger slip further down the pecking order at Anfield.

The Danish international has already made it clear that he does not want to be relegated to the role of squad player and could look for a move away from Liverpool.

Lovren will join up with the rest of the Reds squad for the first time today as they return to training after a two-day break following the club’s US tour.

Liverpool, who have already played seven pre-season friendlies, welcome Borussia Dortmund to Anfield on Sunday for their final warm-up match before they begin their Premier League campaign.