Hutton, a Republic of Ireland under-19 international, arrived at Whaddon Road just over a week ago on a loan deal until the end of the season, but he is due to be released by Spurs in the summer.
He was introduced at half-time in Saturday's 1-0 home defeat to Leyton Orient and Allen is considering his options as he prepares to build for what appears to be a season in League Two.
Allen told the Gloucestershire Echo: "He has been sharp in training and I thought he was terrific.
"He had couple of good chances and he is at his best in final third. He could be one we could take next year."