Context : Mergers between a spiral and an elliptical ( S+E mergers ) are poorly studied so far despite the importance for galaxy evolution . NGC 4441 is a nearby candidate for an advanced remnant of such a merger , showing typical tidal structures like an optical tail and two shells as well as two H i tails . Aims : The study of the molecular gas content gives clues on the impact of the recent merger event on the star formation . Simulations of S+E mergers predict contradictory scenarios concerning the strength and the extent of an induced starburst . Thus , observations of the amount and the distribution of the molecular gas , the raw material of star formation , are needed to understand the influence of the merger on the star formation history . Methods : ^ { 12 } CO and ^ { 13 } CO ( 1-0 ) and ( 2-1 ) observations were obtained using the Onsala Space Observatory 20 m and IRAM 30 m telescope as well as the Plateau de Bure interferometer . These data allow us to carry out a basic analysis of the molecular gas properties such as estimates of the molecular gas mass , its temperature and density and the star formation efficiency . Results : The CO observations reveal an extended molecular gas reservoir out to \sim 4 kpc , with a total molecular gas mass of \sim 5 \cdot 10 ^ { 8 } M _ { \odot } . Furthermore , high resolution imaging shows a central molecular gas feature , most likely a rotating disc hosting most of the molecular gas ( \sim 4 \cdot 10 ^ { 8 } M _ { \odot } ) . This nuclear disc shows a different sense of rotation than the large-scale H i structure , indicating a kinematically decoupled core . We modeled the state of the interstellar medium with the radiative transfer code RADEX , using the ratios of the ^ { 12 } CO and ^ { 13 } CO lines . The results are consistent with a diffuse ( n \leq 10 ^ { 3 } cm ^ { -3 } ) molecular medium with no significant indications for cold and dense cores of ongoing star formation . This is in agreement with the moderate star formation rate of 1 - 2 M _ { \odot } yr ^ { -1 } found in NGC 4441 . Under the assumption of a constant star formation rate , the gas depletion time is \tau = 4.8 \cdot 10 ^ { 8 } yr. NGC 4441 might be a nearby candidate for an early-type galaxy with a dominating A star population , a so-called E+A galaxy , being in a poststarburst phase several 10 ^ { 8 } yr after a merger event . Conclusions :