The reports in several outlets claim Liverpool have made a bid for £40million for the 26-year-old, but that has been rejected by Spanish champions Atletico.
Barcelona are also being linked with a move for Niguez and the player is believed to be one of many names on Liverpool's list of potential signings this summer.
There is no doubt that Niguez would be a fine addition to the Liverpool squad, with his range of passing and proven qualities at the highest levels of the club and international game making him a natural target for the Reds.
Widely hailed as one of the classiest performers in the Spanish league as he helped Atletico win the title last season, with his reported £40million price tag enduring there will be no shortage of clubs interested in his talents.
Liverpool have denied that they will look to replace departed midfielder Gini Wijnaldum, but the continue to be linked with midfielder and
Leicester's Youri Tielemans another player they are believed to have an interest in.
The club are continuing to work on potential transfer moves, with Anfield chiefs keeping their cards close to their chest as leaks from other clubs and agents are fuelling the rumour mill around Jurgen Klopp's transfer plans.
Meanwhile, Virgil Van Dijk, Trent Alexander-Arnold and Joel Matip were involved as Liverpool had their first day of pre-season training in Austria on Monday.
The trio of defenders were among the players undertaking lactate testing, a drill measuring endurance levels with a series of runs, on day one of the pre-season camp on the outskirts of Salzburg.
Van Dijk and Matip were sidelined last season after sustaining injuries in October and January respectively, while Alexander-Arnold sat out England’s Euro 2020 campaign with a thigh problem.
Joe Gomez, another defender who has been on Liverpool’s long-term injured list, is also part of the group that have travelled to Austria.
New signing Ibrahima Konte was also part of the training group in Austria, with the club posting images of him in Liverpool kit on his first official day as a member of Jurgen Klopp's squad.
The Reds have confirmed they are set to have four matches during the camp.
On July 20 they are to play 30-minute ‘mini-games’ behind closed doors against FC Wacker Innsbruck and Stuttgart.
Three days later they will take on boss Jurgen Klopp’s old club Mainz in the Greisbergers Betten-Arena, with a 3,500 capacity.
Then on July 29 they will play Hertha Berlin at the Tivoli Stadium, with a 15,000 capacity.