The Daily Mirror is reporting that both the Reds and Spurs are keen on moves to land the 21-year-old forward in the summer transfer window.
The same story says that Norwich City have already placed a £30m price tag on Maddison after his strong form for the Canaries this season.
According to the same report, Norwich are braced for bids for both Maddison, 21, and winger Murphy.
Maddison has been in fine form for Norwich so far this season and has scored 15 goals in all competitions for the Championship side.
Norwich City are reportedly looking to generate funds from transfer this summer as their parachute payments following their relegation from the Premier League finish this summer.
Liverpool FC are likely to be linked with a host of players in the coming weeks as Jurgen Klopp looks to assemble a squad capable of winning the title this season.
The Reds are currently in third place in the Premier League table this season as they look to try and secure their spot in the Champions League for next season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news