City sealed fourth place in the Premier League with a 1-0 win over Tottenham Hotspur on Tuesday night and Mancini still has hopes of catching Arsenal in third, which would bring with it automatic qualification for the Champions League group stage.
When asked which players he wanted to recruit to strengthen City as they head into Europe's elite competition, Mancini replied: "Cesc Fabregas". The Italian also told The Sun that there is a place at Eastlands for AC Milan striker Ibrahimovic.
Arsenal resisted efforts from Barcelona to prise Fabregas away from Emirates Stadium last summer, but after another season without silverware the focus may be on the Gunners captain once again.
How serious Mancini was is not clear, but he certainly has the financial might to test Arsenal's resolve and will likely spend big.
Ibrahimovic worked under the Italian at Inter Milan and he may be available, having spent this season on loan at AC Milan from Barcelona.
"If Zlatan wants to come to City, I would immediately find a place for him," Mancini said.
"Our target at the start of the season was to qualify for the Champions League and reach a big final - so we have managed to do that.
"As I said when I arrived, in two or three years, Manchester City can become one of the top clubs in Europe. We have everything you need to do this."
City can cap their season with victory in the FA Cup on Saturday, live on ESPN, and the Italian has urged his players to turn their attentions to Stoke.
He said: "Now we must think of the weekend. This latest win will give us a lift for Saturday."