Brendan Rodgers wants to leave a "proud" legacy at Liverpool as he prepares to take charge of the club for the 100th time in the Premier League.
Saturday's Merseyside derby at Everton will see the Reds bid to extend their unbeaten league run to eight matches.
Rodgers says "anything is possible" and is targeting success in the FA Cup, Europa League and a top-four finish.
"At whatever point I leave here hopefully I'll be leaving something people can be proud of," he said.
"We now have to rubber-stamp that by winning some silverware."
Rodgers has won 53, drawn 24 and lost 22 of 99 league matches since taking charge at Anfield in June 2012.
"I've enjoyed every minute of my time here. These two and a half years have been a great experience and I think the football club have moved forward," he added.
"We are in a European competition and in the FA Cup we can get to final. We can challenge not just for fourth place but beyond that. Those are the objectives of the forthcoming months."
Liverpool travel to Crystal Palace in the FA Cup fifth round on 14 February after beating Bolton 2-1 on Wednesday, then host Besiktas in the last 32 of the Europa League round the following Thursday.
Rodgers on the Merseyside derby
"Derby games are very exciting. They are wonderful games to be involved in, full of emotion and they go so fast.
"The quality of the football is outstanding, which is especially impressive as the players are under intense pressure."
On whether Daniel Sturridge could start
"Daniel, like every player, wants to play. He is coming along very well.
"We'll analyse whether he starts over the next couple of days."
On Everton fans being glad to see the back of LA Galaxy-bound Steven Gerrard
"I'm sure they will. He has been incredible for the club and been outstanding in so many derby games.
"How will he deal with the emotion of it being his last? Like he has all the others - by being focused on the team getting a result."