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.
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