Spurs boss Mauricio Pochettino worked with Lallana at Southampton, and the paper claim he attempted to bring him to White Hart Lane in 2014, only to be pipped by Liverpool, who at the time were able to offer Champions League football.
Tottenham's place in the competition is assured next season, with Liverpool relying on beating Sevilla in the Europa League final to qualify.
Pochettino is so keen on the England international he is claimed to have asked chairman Daniel Levy to prioritise his acquisition above any other.
The Sun's report states: "The Tottenham boss will ask chairman Daniel Levy to make the Liverpool midfielder his No1 target when the window opens."
A tale of two managers
Lallana enjoyed success under Mauricio Pochettino at Southampton, with his form good enough to convince Liverpool to spend £25 million on bringing him to Anfield.
He has improved this campaign after an injury hit first season for the Reds, but it remains unclear just how highly Jurgen Klopp values him.
Klopp has used him as part of the squad and even starting him in some big games, but the German has not yet had a full summer transfer window with which to buy players, and has obviously spent the past few months planning on strengthening the squad.
Lallana's future will depend on Klopp's plans, and if the midfielder feels he will get substantially more first team starts at one club than another, while Liverpool will have to weigh up whether they want to sanction a move to a Premier League competitor.