Following the winter break and last weekend's Coupe de France ties - in which PSG beat Brest 5-2 with an Ibrahimovic hat-trick - clubs return to league action this weekend.
The capital club top the table by three points, though Monaco can move level if they win at Montpellier on Friday evening.
And Ibrahimovic, the league's top scorer with 15 goals in 18 games, said: "I hope to improve my game and become even better in 2014.
"As a squad, we want to win all the trophies we're aiming for and make Paris and our fans happy.
"With a hat-trick, I couldn't have started the year in a better way. Now the important thing is to continue like that. Everyone is in form and we have to continue like that, there are a lot of games waiting for us."
Third-placed Lille take on Reims on Sunday while St Etienne, who won their rearranged game against Evian on Wednesday to go fourth, travel to Guingamp on Saturday.
ASSE coach Christophe Galtier told the club's website: "We have finished the first half of the season with 33 points. That's very good. Now we must continue to be ambitious."
Les Verts' win relegated Bordeaux to fifth but they go into their derby against Toulouse unbeaten in eight games domestically, with six wins in that sequence.
Tefece midfielder Pantxi Sirieix is aware of the tough test facing his side but told L'Equipe: "In derbies, you have to win, that's it. It's important for the supporters and for supremacy in the south-west.
"Les Girondins are confident after a good run. We have to be strong to win points there."
Saturday's other games see Lyon host Sochaux while Rennes face Nice and Bastia travel to Valenciennes.
As well as Lille's game on Sunday, Lorient travel to Nantes looking to bounce back from their shock cup exit to fourth-tier Yzeure by extending their eight-match unbeaten league run.
Marseille take on an Evian side possibly featuring one of their own in Modou Sougou, who is on loan from the Stade Velodrome to Les Roses.
Sougou told etgfc.com: "It will be a special game for me, but for all the team in fact because Marseille are a big club.
"Everyone enjoys playing these matches. We have to do all we can to win this game, we are in a survival situation."