The 42-year-old has impressed in his first coaching role since taking over at Ajax from Martin Jol in 2010, leading the Amsterdam giants to back-to-back league titles, and was targeted by Spartak last month after they sacked their Spanish coach Unai Emery.
"Spartak Moscow wanted [De Boer] to take over immediately and some clubs see him as the ideal trainer for next summer. But he has no interest," Overmars told De Telegraaf.
After seeing the former Netherlands international turn them down, Spartak have once again turned to director of football Valery Karpin to take over as caretaker manager until the end of the season.
This is the second time that Karpin has taken the Spartak hotseat on a temporary basis. In 2009 he replaced Michael Laudrup, now manager of Swansea City, after poor run of results and stayed in charge until May this year when Emery was hired.
Ajax, who play Utrecht on Sunday, currently lie third in the Eredivisie table, four points behind leaders PSV.