The goal also saw the Egypt worldwide reach the 40-goal mark across all competitions; a feat that he achieved in just 45 games.
The Reds star is battling it out with Manchester City Kevin De Bruyne for the PFA Player of the Year award.
"If you had a choice?"
Burnley earned their fifth straight league win with a 2-1 victory over Leicester City at Turf Moor to boost their chances of possible Europa League qualification. "I'm sure he'll keep doing that for the rest of the season".
He added: "Of course I can not lie - it is in my mind".
"But you know, you can see [against Bournemouth] with the team everyone tries to pass the ball to me to help me".
Salah needs another eight goals to pass Rush's record of 47 from 1983-84 - a season in which Liverpool won both the domestic title and the European Cup.
Liverpool forward Mohamed Salah says a Champions League win would mean more to him than any individual honours he may claim this season.
You could nearly see the joy in Henderson's eyes as he was asked to comment on Salah's goalscoring.
They had appealed the Premier League Match Centre's call to hand Christian Eriksen the goal, with Kane arguing the Dane's free-kick had brushed his shoulder, and the overturning of the decision prompted Salah to respond with surprise on social media. I don't want anything about that. "We had the first one against United, we could not do it and now we have another one against Swansea with our 60,000 people and we are going to try to be champion".
"You could see in the last 10 or 15 minutes how intense it was for the boys. Hopefully they all stay healthy and then we know we can play good football but we need a little bit of luck because we don't have 25 players in the squad any more".
Bournemouth manager Eddie Howe was in awe of Liverpool, meanwhile, admitting his side struggled to make a fist of the match.
It took only seven minutes for the hosts to open the scoring, with Sadio Mané netting at the second time of asking after his header was saved by Asmir Begovic.
There was still time for Roberto Firmino to add to Liverpool's tally with a late third goal, cutting in from the left and firing a low right-footer past Begovic after collecting a pass from Alex Oxlade-Chamberlain.