Chief executive Ian Ayre has flown to Spain to try and complete the transfers, which would take Liverpool's summer spending through the £100m barrier if completed.
The deal for Manquillo is reported to be a loan, possibly for two seasons, with a permanent deal worth in the region of £6m following at the end of that.
Moreno, who like Manquillo, has also been linked with Arsenal this summer, is expected to cost the Reds £20m.
Boss Brendan Rodgers has enjoyed a fruitful summer with six signings already completed at the cost of around £90m; Rickie Lambert, Adam Lallana and Dejan Lovren have arrived from Southampton along with Lille striker Divock Origi, Bayer Leverkusen midfielder Emre Can and Benfica winger Lazar Markovic.
Rodgers hinted after the penalty shootout win over Manchester City on Thursday morning that more deals were in the works.
"We still have some business to do," he said.
"We have some positions that we want to fill so by the end of August we’ll have a strong squad to go forward with."