The Egyptian has been in red-hot form this season, netting 21 goals in 25 top-flight appearances, including a brace in Monday's (AEDT) dramatic 2-2 with Kane's Tottenham.
Kane netted a stoppage-time penalty at Anfield - having seen an earlier spot-kick saved - to take his league tally for 2017-2018 to 22 from 25 matches.
With Manchester City's Sergio Aguero (17) third on the list of Premier League goalscorers, Salah and two-time Golden Boot winner Kane appear set to battle it out over the final dozen games.
"He [Kane] is a great player, in the last two years he has already been the top scorer," Salah told Marca.
"Kane plays as a number nine and has more chances to score goals than me. In my mind I want to win it, but we will see what happens."
After a failed previous stint in the Premier League with Chelsea, Salah believes he is in the form of his career.
He said: "I didn't do well [at Chelsea] because I didn't play many games. I was there for one year, but I only played during the first six months.
"After that, I hardly participated. I went to Fiorentina, scored goals, then in Rome I played very well and returned to England."
Salah sees no reason why Liverpool cannot challenge for the UEFA Champions League - its only remaining shot at a trophy this season - ahead of a last-16 tie with Porto.
"For us as a club and as a team it is very important to get through. We need to qualify," he said.
"There is no extra pressure because for us every game is important; Premier League, cups, Champions League ... of course this competition is something different for the club and the fans but the team tries in every match to give 100 per cent. It will be an important game against a great team, and we will have to give more than them to win.
"I have already commented that in football anything can happen ... we will try to work hard in each match and win it."