The impact of the interface phenomena on the properties of nanostructured materials is the focus of modern physics. We studied the magnetic properties of the nanostructured In–Ag alloy confined within a porous glass. The alloy composition was close to the eutectic point in the indium-rich range of the phase diagram. Temperature dependences of DC magnetization evidenced two superconducting transitions at 4.05 and 3.38 K. The magnetization isotherms demonstrated the superposition of two hysteresis loops with low and high critical fields below the second transition, a single hysteresis between the transitions and ferromagnetism with weak remanence in the normal state of the alloy. The shape of the loop seen below the second transition, which closes at a low magnetic field, corresponded to the intermediate state of the type-I superconductor. It was ascribed to strongly linked indium segregates. The loop observed below the first transition is referred to as type-II superconductivity. The secondary and tertiary magnetization branches measured at decreasing and increasing fields were shifted relative to each other, revealing the proximity of superconducting and ferromagnetic phases at the nanometer scale. This phenomenon was observed for the first time in the alloy, whose components were not magnetic in bulk. The sign of the shift shows the dominant role of the stray fields of ferromagnetic regions. Ferromagnetism was suggested to emerge at the interface between the In and AgIn2 segregates.