Moreno is a man in demand. A number of clubs including Southampton and Real Sociedad have made enquires over the availability of the 24-year-old while Napoli had an £11million offer reportedly rejected.
But we understand the Swans, in an attempt to jump to the front of what's quickly becoming a long queue, have made a bid that is just under the £13million mark.
Liverpool are yet to respond to the formal offer and it and is thought the club want a minimum of £15million for former Sevilla defender, who is now surplus to requirements at Anfield.
With a potential bidding war on their hands, and over two months of the transfer window still remaining, it's unlikely the club will part ways for anything under that figure.
Moreno, who cost £12.5million when he signed for the Merseyside club in the summer of 2014, has made over 100 appearances for Liverpool but was the understudy to makeshift left-back James Milner last season and made just the two starts in the Premier League.
And with Jürgen Klopp and the recruitment team at Anfield actively seeking to bring in a left-back this summer, the Spaniard's time at Anfield is up.
But clearly the potential he showed during his time in La Liga, coupled with his positive performances in Klopp's debut campaign, is enough for several clubs to be interested in his services this summer.