The 24-year-old has set the Dutch Eredivisie alight with AZ Alkmaar, and his time with the Dutch title challengers could be coming to an end, according to the Mirror.
"[LFC manager] Kenny Dalglish is well aware of Elm's power-packed ability and will finalize his summer recruitment drive with his club's owners, the Fenway Group, at the end of the season," the report says.
"The good news about Elm, who resembles Anfield skipper Steven Gerrard with his shooting power at set pieces, is that, with only one year to go on his current contract, he can be lured away for around £8 million ($13 million)."
Elm has drawn interest from LFC and a number of top clubs from Spain, England, Italy and Germany.
He turned professional in 2005 with Swedish club Kalmaar FF. He spent four and a half years with his first club and represented his country from the U-17 through senior levels.
In 2009, Elm made the jump to the Eredivisie when he joined then-champion AZ Alkaar in the summer. He became an instant starter with the fashionable Dutch club, helping it achieve fifth and fourth place finishes in the last two seasons.
The 2011-12 campaign has been a breakout one for the center midfielder. He has made 50 appearances (in all competitions), scoring 13 goals and setting up 17 more.
Elm has played 22 times for Sweden, scoring once. Barring injury, he will play a key role with the Sweden team at this summer's European Championship.
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