The Gills boss has identified the 29-year-old as a transfer target after he scored 21 goals for the Daggers last season, and it was reported that the Kent club had bid £150,000 for the player earlier this week.
But Stimson said: "We have put a bid in for Benson which we were told by his representative the club would accept.
"The club refused it and then it went national mentioning some crazy figure of £150,000. We haven't got that kind of money.
"We're still interested in the kid, it's just a matter of his advisers now talking to the club and hopefully Dagenham - from what I'm led to believe - honouring what they told the kid at the end of last season. If that's the case he would be coming to join us."