The Reds enjoyed a good start to the 2016/17 season and continued their impressive run until the first half of the season. However, they have struggled in all competitions in this calendar year as they were knocked out of the EFL Cup and the FA Cup and have also failed to mount any challenge to Chelsea in the title race.
According to The Sun, Liverpool are looking to bolster their squad in order to become a serious contender for the title next season. The club's chiefs believe it is necessary for the Merseyside club to add more depth to the squad and are looking to help Jurgen Klopp in the transfer market.
The former Borussia Dortmund manager has set his sights on Real's Rodriguez and Asensio and both the players could be allowed to leave the Spanish capital club following this campaign.
Asensio joined Real from Mallorca in 2014 and spent the last two seasons on loan at his former club and Espanyol. He has started in six league games for the 11-time European winners, while Rodriguez has one more start than the Spain international in the La Liga this season.
Lack of playing time at Santiago Bernabeu has seen Rodriguez and Asensio attract interest from other clubs from Europe. Liverpool are looking at the option of securing the services of both the midfielders and will have to splash around £92m ($114.8m) in bringing them to Anfield.
Rodriguez has attracted interest from Chelsea, Manchester United and Arsenal. However, the South American star has expressed his desire to continue with his current employers after ruling out a summer exit.
According to the Spanish newspaper AS, Zinedine Zidane is a huge admirer of Asensio and wants to keep him at the club despite strong interest from England and Italy. Arsenal, United and Chelsea, along with Juventus are believed to interested in signing the midfielder.
With competitions for Rodriguez and Asensio, it should be seen whether Liverpool will be able to beat their league rivals in signing Real's midfield duo. The Reds' chances of attracting top talents will improve if they qualify for the next season's Champions League.
Klopp's side are currently sitting in the fourth place in the league table with 56 points after 29 games. Liverpool are four points ahead of fifth place United, who have an advantage of two games in hand.