The Spain international forward was once regarded as one of the most promising young players in Europe, and was valued at more than £35million three years ago when he signed for Roma.
The Reds are confident they can bring the 23-year-old to the Premier League for as little as £5million.
Krkic is currently on loan at Ajax, where Anfield scouts have been running the rule over him in recent weeks.
The youngster’s value has dramatically dropped after an unhappy move to Roma, where he was quickly loaned out to AC Milan, and then bought back by Barcelona, who took advantage of a buy-back-clause last summer.
The versatile forward had hoped to revive his career at the Nou Camp, but has since been sent on loan to the Dutch champions.
He admitted last week his future is still up in the air, as he is unsure whether his deal with the Amsterdam giants will be made permanent.
“We’ll see about my future, there are still two months of the season to go before any decisions have to be made,” he explained.
Krkic made the switch to Roma in 2011, with the Italian club agreeing to make a down-payment of £11m, plus a further £25m should they wish to secure his long term future.