  Context: The stellar production of the light element lithium is still a
matter of debate.
  Aims: We report the detection of low-mass, Li-rich Asymptotic Giant Branch
(AGB) stars located in the Galactic bulge.
  Methods: A homogeneous and well-selected sample of low mass, oxygen-rich AGB
stars in the Galactic bulge has been searched for the absorption lines of Li.
Using spectral synthesis techniques, we determine from high resolution UVES/VLT
spectra the Li abundance in four out of 27 sample stars, and an upper limit for
the remaining stars.
  Results: Two stars in our sample have a solar Li abundance or above; these
stars seem to be a novelty, since they do not show any s-element enhancement.
Two more stars have a Li abundance slightly below solar; these stars do show
s-element enhancement in their spectra. Different scenarios which lead to an
increased Li surface abundance in AGB stars are discussed.
  Conclusions: Of the different enrichment scenarios presented, Cool Bottom
Processing (CBP) is the most likely one for the Li-rich objects identified
here. Self-enrichment by Hot Bottom Burning (HBB) seems very unlikely as all
Li-rich stars are below the HBB mass limit. Also, the ingestion of a low mass
companion into the stars' envelope is unlikely because the associated
additional effects are lacking. Mass transfer from a former massive binary
companion is a possible scenario, if the companion produced little s-process
elements. A simple theoretical estimation for the Li abundance due to CBP is
presented and compared to the observed values.
