Integer correlation conjecture for Kloosterman sums and cusp-form eigenvalues

Let $f$ be a fixed primitive cusp form, holomorphic or Maass, and let $\lambda_f(n)$ denote its Hecke eigenvalue at $n$. Write $\mathcal{L}=\log X$. Integer correlation conjecture. For all sufficiently large $X$,

$$\sum_{n\leq X}\lambda_f(n)\mathrm{Kl}(1,n)=O\left(X\mathcal{L}^{-2018}\right).$$

This is a conjectured power-logarithmic saving for the correlation over consecutive integers. The source gives no evidence of a proof or disproof, so the conjecture remains open.