According to Neil Moxley of the Sunday Mirror, the Reds will confirm the capture of Robertson when the transfer window opens in the summer. The Scotland international only has one year left to run on his contract with the Tigers.
As well as the full-back, Maguire is also rumoured to be on Liverpool's radar.
"Promoted Newcastle [United] have long been interested in the former Sheffield United trainee, and now they have been joined by Liverpool and Champions League-bound Tottenham," Moxley noted.
Robertson would be an intriguing option for Liverpool, as the Reds have utilised midfielder James Milner at left-back for much of the season. Manager Jurgen Klopp doesn't appear to have total faith in deputy Alberto Moreno, either.
The Scot would at least be another natural option for Liverpool to call upon, and given the full-back's contract situation, coupled with Hull's potential relegation, the Reds may be able to snap him up for a bargain amount.
Football journalist Ell Bretland is a big fan of the 23-year-old, noting his all-around ability:
The defensive portion of the Liverpool team is an area that needs to be strengthened, with the good work in the final third by the Reds often undone by their poor play at the base of the XI.
Maguire is another fascinating target. Like Robertson, he's stood out in a struggling Hull side. Since Marco Silva arrived at the club in January, the centre-back has been a talisman.
The 24-year-old is vocal, physical and seems to love defending. But there's a composure on the ball that's made Maguire stand out, as he's able to take his time over distribution and get Hull moving forward with some intelligent passing.
Neil Atkinson of the Anfield Wrap doesn't feel as though Maguire has been given the credit he deserves this season:
With the Reds set to take part in European football again next season, it's imperative they bring in players to add depth to the squad. However, there's an argument to say that both Robertson and Maguire would be pushing for first-team places at Anfield.
Each player ticks a lot of positive boxes. Maguire and Robertson are young, familiar with the Premier League and have the potential to improve.
As these numbers from Sky Sports Statto illustrate, Liverpool need to make significant adjustments in their back four:
Still, if Liverpool do get into the UEFA Champions League next season, there will be a thirst from the fanbase to see some big-name players come through the door. While Robertson and Maguire are both capable footballers, their arrivals wouldn't get pulses quickening on Merseyside ahead of what should be a fascinating 2017-18.
Provided the Hull duo aren't Klopp's marquee acquisitions, both would be decent captures. Robertson would bring dynamism, industry and pace to the left flank, while Maguire has the quality to push the likes of Dejan Lovren and Joel Matip for a place in the heart of the defence.