Downing had to force his way into the starting XI last season before establishing himself and going on to make 28 league appearances.
New boys Iago Aspas and Luis Alberto will both be competing for a wide berth this term, but Downing is happy to see them onboard.
He told the club website: "They're nice lads. They're very quiet, but it's their first week at the club, so they're not used to the area, the lads and how we train. But you can see they're enjoying it.
"You need at least two or three players in every position to keep people on their toes, especially at a club like this.
"We're fighting on many fronts - cup competitions and the league - so you have to be strong in every department. But competition brings the best out of players, and hopefully it will in me.
"My targets will be similar to when I got back into the team last season - enjoy it, work hard and play some good football like we did at the end of last season.
"If we play like that again as a team, we've got a real chance of success. For me personally, I've just got to keep going."
Liverpool returned to pre-season training on Tuesday and Downing added: "We've had six weeks off, but the lads were all looking forward to getting back.
"There have been new signings come in and there's a bit of a buzz around the place. We can't wait to get started now and get the games underway."