Context : The quest for hot dust in the central region of debris disks requires high resolution and high dynamic range imaging .
Near-infrared interferometry is a powerful means to directly detect faint emission from hot grains .

Aims : We probed the first 3 AU around \tau Ceti and \epsilon Eridani with the CHARA array ( Mt Wilson , USA ) in order to gauge the 2 \mu m excess flux emanating from possible hot dust grains in the debris disks and to also resolve the stellar photospheres .

Methods : High precision visibility amplitude measurements were performed with the FLUOR single mode fiber instrument and telescope pairs on baselines ranging from 22 to 241 m of projected length .
The short baseline observations allow us to disentangle the contribution of an extended structure from the photospheric emission , while the long baselines constrain the stellar diameter .

Results : We have detected a resolved emission around \tau Cet , corresponding to a spatially integrated , fractional excess flux of 0.98 \pm 0.21 \times 10 ^ { -2 } with respect to the photospheric flux in the K ^ { \prime } –band .
Around \epsilon Eri , our measurements can exclude a fractional excess of greater than 0.6 \times 10 ^ { -2 } ( 3 \sigma ) .
We interpret the photometric excess around \tau Cet as a possible signature of hot grains in the inner debris disk and demonstrate that a faint , physical or background , companion can be safely excluded .
In addition , we measured both stellar angular diameters with an unprecedented accuracy : \Theta _ { LD } ( \tau { Cet } ) = 2.015 \pm 0.011 mas and \Theta _ { LD } ( \epsilon { Eri } ) = 2.126 \pm 0.014 mas .

Conclusions :