Let \(Q\) be a real indefinite quadratic form in 3 or more variables whose coefficients are not all in rational ratio. It was proved by Margulis (1987) that \(Q\) assumes arbitrarily small values at integral points. In this paper a natural analogue of Margulis result has been investigated. Davenport and Lewis (1972) remarked that if one considers the special case in which the form is diagonal and the number of variables \(s\) is at least 5, then the gaps between successive values of the form at integer points approach zero as the values grow large. This follows from a result of Jarník and Walfisz (1930). Estermann proposed the analogous question for general forms allowing that 5 may have to be replaced by some large number. Recently \textit{V. Bentkus} and \textit{F. Götze} [Ann. Math. (2) 150, No. 3, 977--1027 (1999; Zbl 0979.11048)] answered the question positively with 9 needed to replace 5. Unaware of their result the author also answers the question positively, but only in the special case when the coefficients of the form are algebraic. The result is as follows: Suppose that \(s\) is a positive integer with \(s\geq 416\). If \(Q\) is a positive definite form in \(s\) variables with real algebraic coefficients not all in rational ratio, then for any \(\varepsilon>0\), there is a real number \(M=M(Q,\varepsilon)\) such that for any real number \(N\geq M\), there exist integers \(y_1,\dots,y_s\) satisfying \[ \bigl| Q(y_1, \dots,y_s)-N\bigr|<\varepsilon. \] The main idea of proof depends upon choosing integral vectors so that on their span, the original form can be written as a sum of a diagonal form, a binary form and a small error term. By completing the Davenport-Heilbronn (1946) method while controlling the size of the error term the desired result is proved.