Expectiles are least-square analogues of quantiles. They have received a fair amount of attention due to their potential for application in financial, actuarial, and economic contexts. Some recent work has focused on the application of extreme expectiles to assess tail risk, and on their estimation in a heavy-tailed framework. We investigate the estimation of extreme expectiles of a heavy-tailed random variable $Y$ given a high-dimensional covariate $X$. We derive generic conditions under which the limiting behaviour of our estimators can be established. Applications are presented to some regression models. A finite-sample study illustrates the behaviour of our procedures in practice.