  The present paper reports a holographic reconstruction scheme for
$f(T,\mathcal T)$ gravity proposed in Harko et al. $\emph{JCAP}\; 12(2014)021$
where $T$ is the torsion scalar and $\mathcal{T}$ is the trace of the
energy-momentum tensor considering future event horizon as the enveloping
horizon of the universe. We have considered $f(T, \mathcal T)=T + \gamma
g(\mathcal T)$ and $f(T,\mathcal T) =\beta \mathcal T + g(T)$ for
reconstruction. We observe that the derived $f(T,\mathcal T)$ models can
represent phantom or quintessence regimes of the universe which are compatible
with the current observational data.
