Stevenage chairman Phil Wallace believes new manager Gary Smith is capable of leading the club to a third successive promotion.
And Boro are currently in sixth place, chasing a berth in the Championship.
"It would be a fairy tale and remarkable but it's what we're going for," Wallace told BBC Look East.
"Is it possible? Absolutely. Gary's his own man and will come in and do his own job.
"We're very grateful for the success we've had under Graham for three-and-a-half years. It's been remarkable and now it's all about getting into the Championship."
Westley took Stevenage to their highest ever standing in the football pyramid and became renowned for his unorthodox methods at Broadhall Way.
The former Wycombe striker insisted his squad trained from nine in the morning until five in the evening, whereas most clubs finish their sessions at lunchtime.
And Smith, himself an ex-Chairboy who went on to lead Colorado Rapids to MLS Cup victory in 2010, will have to decide whether to adhere to the ethos left behind by his predecessor.
"The guys have probably been used to a certain schedule and regime," he explained.
"I certainly don't want to change too much. But I'll have a good chat with some of the guys and they'll give me some views on what has been happening and how they have been working.
"There's certainly been something right going on. So I won't make too many changes."
Meanwhile, former Bournemouth and Fulham defender Mark Newson has been named as Smith's assistant.
He played alongside Smith at Barnet in the mid-1990s ad has coaching experience at West Ham and Crystal Palace.