Belgian Prime Minister, Herman van Rompuy, is many people's favourite for the post of EU president, which under the treaty has a term of office lasting two and a half years, re-electable once.
Speaking in Berlin on Monday where he was attending the 20th anniversary celebrations of the fall of the Berlin Wall, Reinfeldt said he was ringing round the heads of the other 26 member states to canvas their preferences.
On the Swedish government's EU presidency homepage, Reinfeldt writes,
"I am half-way through my consultations. When I have spoken to everybody and have a better overview of the situation I will invite my colleagues for an extra summit in Brussels."
That summit is expected to be held this month. The treaty of Lisbon comes into force on December the first.