In this article, we explore the possibility of inheriting an almost Ricci soliton structure on a compact Riemannian manifold \(\left( M^{n},g\right) \) of dimension n through an isometric embedding of \(\left( M^{n},g\right) \) into the Euclidean space \(\left( R^{m},{\overline{g}}\right) \) , \(m>n\) . For achieving this goal, we choose a constant unit vector \(\overrightarrow{a}\) on \(R^{m}\) with its tangential component \(\zeta \) and normal component \({\overline{N}}\) , and call \(\zeta \) the KN-vector, \({\overline{N}}\) the KN-normal. We use a lower bound involving a smooth function f on \(M^{n}\) on the integral of the Ricci curvature \(Ric\left( \zeta ,\zeta \right) \) with respect to the KN-vector \(\zeta \) to show that \(\left( M^{n},g,\zeta ,f\right) \) is almost Ricci soliton, which is called the KN-almost Ricci soliton. The mean curvature vector H, gives a natural function \(\varphi ={\overline{g}}\left( H,{\overline{N}}\right) \) on the KN-almost Ricci soliton \(\left( M^{n},g,\zeta ,f\right) \) called KN-function. Then, we find a condition involving the KN-function \(\varphi \) to show that an n-dimensional compact proper KN-almost Ricci soliton \(\left( M^{n},g,\zeta ,f\right) \) , \(n>2\) , is isometric to the sphere \(S^{n}(c)\) . In this article, we also find conditions which make a compact KN-almost Ricci soliton \(\left( M^{n},g,\zeta ,f\right) \) trivial. In first result in this direction, we show that a compact n-dimensional KN-almost Ricci soliton \(\left( M^{n},g,\zeta ,f\right) \) , \(n>2\) , with KN-function \(\varphi \) and Ricci curvature in the direction of \(\zeta \) bounded below by \(-(n-1)\zeta \left( \varphi \right) \) is either isometric to the sphere \(S^{n}(c)\) or else it is a trivial Ricci soliton. Finally, we show that a compact n-dimensional KN-almost Ricci soliton \(\left( M^{n},g,\zeta ,f\right) \) , \(n>2\) , having scalar curvature \(\tau \) and KN-function \(\varphi \) satisfying \(\tau \varphi \ge 0\) is necessarily a trivial Ricci soliton.
