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Reds manager Brendan Rodgers is targeting at least one new striker when the transfer window opens in January, with Luis Suarez being the club's only option up front at present.
Athletic Bilbao hitman Fernando Llorente and Valencia poacher Roberto Soldado are just two of the players who have been linked with moves to Anfield, but both would blow huge holes in Rodgers' modest budget.
Instead, the club are said to have turned to Lyon powerhouse Gomis, who has a proven record as a goalscorer - bagging at least 10 in each of the last six seasons.
The 27-year-old looks like he will add this season to that list too, having already scored nine times, leading to speculation of a move away.
That talk has intensified in the last few days, with scouts from a number of clubs watching Gomis score a stunning hat-trick for Lyon in midweek.
One of the watching sides was Liverpool, who have now made an approach to Lyon to try and negotiate a deal, according to French magazine Le 10 Sport.
The publication claims Liverpool representatives have offered around £8million for the striker, who has 10 caps for France and has previously been linked with Real Madrid.