And initial indications were that, following surgery, the 25-year-old Annan captain and defender would be out of action for six months.
But the club now say: "Kevin is making rapid progress and hopes he will be able to play with a protective mask."
Neilson, who began his career with Dalbeattie Star and Threave Rovers in the South of Scotland League, has been a regular in Annan's first team since they joined the Scottish Football League in 2008.
Kevin is making rapid progress and hopes he will be able to play with a protective mask
Annan statement
It was possible he might miss the start of their third season in Division Three.
But Annan's website stated: "It looks like captain Kevin Neilson will be able to start pre-season training with the rest of the squad on 17 June.
"Kevin suffered an horrific accident at work and had to have a metal plate inserted through a cut to the side of his eye before attaching it to his skull.
"Kevin is making rapid progress and hopes he will be able to play with a protective mask."
Meanwhile, Annan have signed striker Pat Walker on a one-year contract after the 25-year-old left Albion Rovers following four seasons with their Third Division rivals.
He became manager Harry Cairney's second close-season capture after 32-year-old Andy Aitken rejoined his hometown club on a two-year deal following his departure from Ayr United.
The defender had left Annan to join local rivals Queen of the South aged 16.
Source: BBC Sport
>> Terms & Conditions