The Reds take on Manchester United this weekend and Evans believes Kenny Dalglish can level the clubs' number of title wins after Sir Alex Ferguson's side won their 19th last season to finally surpass Liverpool.
Evans told BBC Sport: "We could do it this year, never write Liverpool off.
"You have got to believe you can win it. There's no point being in it if you don't think you can win it, certainly at Liverpool's level - that's where you've got to be.
"You've got to have in your mind that, if you went on a bit of a run, you have got a chance.
"There's still plenty of football to go. Liverpool play Manchester United on Saturday at Anfield and, if we beat them, it will set them back a little bit and give us lots of confidence."
Evans won 12 league titles during his 33-year Liverpool career and thinks that John W. Henry's investment in the squad and other rivals' bad form could open up a spot for the Reds.
"Liverpool are going the right way, they are going forward - and I think it's been a fantastic year under John Henry," Evans continued."Manchester United look strong and Manchester City are progressing but a few of the others seem to have dropped away.
"Arsenal don't seem to be what they were and Tottenham are just starting to find their feet after a slow start. If we can get ourselves in that top four where we should be, that will be great progress."