We present CO(1-0) and CO(2-1) maps of the interacting barred LINER/Seyfert 2 galaxy NGC 3627 obtained with the IRAM interferometer at resolutions of 2.1 x 1.3 and 0.9 x 0.6, respectively. The molecular gas emission shows a nuclear peak, an elongated bar-like structure of ~18 (~900 pc) diameter in both CO maps and, in CO(1-0), a two-arm spiral feature from r~9 (~450 pc) to r~16 (~800 pc). The inner ~18 bar-like structure, with a north/south orientation (PA = 14{deg}), forms two peaks at the extremes of this elongated emission region. The kinematics of the inner molecular gas shows signatures of non-circular motions associated both with the 18 bar-like structure and the spiral feature detected beyond it. The 1.6 micron H-band 2MASS image of NGC 3627 shows a stellar bar with a PA = -21{deg}, different from the PA (= 14{deg}) of the CO bar-like structure, indicating that the gas is leading the stellar bar. The torques computed with the HST-NICMOS F160W image and our PdBI maps are negative down to the resolution limit of our images, ~60 pc in CO(2-1). If the bar ends at ~3 kpc, coincident with corotation (CR), the torques are negative between the CR of the bar and the nucleus, down to the resolution limit of our observations. This scenario is compatible with a recently-formed rapidly rotating bar which has had insufficient time to slow down because of secular evolution, and thus has not yet formed an inner Lindblad resonance (ILR). The presence of molecular gas inside the CR of the primary bar, where we expect that the ILR will form, makes NGC 3627 a potential smoking gun of inner gas inflow. The gas is fueling the central region, and in a second step could fuel directly the active nucleus.
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