The Reds finished second in the league last season, just three points from winning the title outright, with Manchester City eventually finishing first.
Much has been made of whether Liverpool will be able to replicate that kind of challenge this time around, especially after the £75 million summer sale of star man Luis Suarez.
However, while Lovren admits he cannot categorically say his side will win the title, he insists they will be fighting alongside the likes of Manchester City, Chelsea and Manchester United.
"I can't say now that we can win the title," he told reporters, "but I will say that we have a really good chance along with Chelsea, Arsenal, Manchester United and Manchester City. I think it will be tight but we will be here fighting."
Lovren is in line to start against former side Southampton this Sunday in Liverpool’s Premier League opener.
The 25-year-old has made a strong start to life at Anfield, scoring on his debut in the 4-0 friendly win over Borussia Dortmund.
Intriguingly, Lovren also scored at Anfield last season – for Southampton, when the Saints subjected the Reds to a 1-0 defeat, one of just two all season at home.
Lovren does, though, face plenty of competition for his place in Rodgers’ side, with Martin Skrtel, Mamadou Sakho, Kolo Toure and more rivalling him for the centre-back spot.
Daniel Agger could also challenge him for a place in the starting XI, although he is unavailable for selection against Southampton.