Context: Quantifying the gas content inside the dust gaps of transition disks is important to establish their origin. Aims: We seek to constrain the surface density of warm gas in the disk of HD 139614, a Herbig Ae star with a transition disk exhibiting a dust gap from 2.3 to 6 AU. Methods: We have obtained ESO/VLT CRIRES high-resolution spectra of CO ro-vibrational emission. We derived constraints on the disk's structure by modeling the line-profiles, the spectroastrometric signal, and the rotational diagrams using flat Keplerian disk models. Results: We detected v=1-0 12CO, 2-1 12CO, 1-0 13CO, 1-0 C18O, and 1-0 C17O ro-vibrational lines. 12CO v=1-0 lines have an average width of 14 km/s, Tgas of 450 K and an emitting region from 1 to 15 AU. 13CO and C18O lines are on average 70 and 100 K colder, 1 and 4 km/s narrower, and are dominated by emission at R>6 AU. The 12CO v=1-0 line-profile indicates that if there is a gap in the gas it must be narrower than 2 AU. We find that a drop in the gas surface density (delta_gas) at R<5-6 AU is required to simultaneously reproduce the line-profiles and rotational diagrams of the three CO isotopologs. Delta_gas can range from 10^-2 to 10^-4 depending on the gas-to-dust ratio of the outer disk. We find that at 12 AU) gas gap suggest the presence of an embedded <2 MJ planet at around 4 AU.
Comment: accepted for publication in A&A; 30 pages (including Appendix), 24 figure; v2-v4: text corrections