The 'Reds' finished 25 points behind champions Manchester City in the Premier League last season, though this year have begun brightly with four wins from four.
Jurgen Klopp's side have been referred to as Pep Guardiola's main rival this season as the 'Citizens' chase back-to-back league titles.
27-year-old Wijnaldum has warned Liverpool fans not to get carried away with their expectations.
Speaking to 'The Telegraph', the Dutchman said: "We were not really in a competition with Man City in the Premier League last season. When you are 25 points behind, it is not competing.
"But all I can tell you as a player is I am happy when a player like Virgil [van Dijk] signs and walks into the dressing room because then you think, 'yeah, we can really achieve something with this team.'
"We are doing everything we can. I can only say we hope to do it. There is no point going through this season saying, 'come on, come on, we have to win something, we have to win something.
"We need to do the right things to get us into that position, to give us that chance. Looking too far ahead is a mistake.
"The reason everyone is saying it this year is because of the signings.
"The expectation from outside is much bigger than previous years because we spent some money. We lost [Philippe] Coutinho [to Barcelona], but signed three or four top players."
Liverpool will hope to continue their early-season form as they take on Tottenham Hotspur on Saturday.