Ormerod is currently a free agent after leaving Conference side Wrexham at the end of last season and the 37-year-old has accepted the invitation to train with Stanley.
Ormerod started his career as a youth player at Blackburn Rovers before joining Accrington in non-league in 1995.
The forward earned a move into the Football League with Blackpool two years later, with the transfer helping to fund the building of the main stand at the Crown Ground.
Ormerod later moved on to Southampton, where he played alongside Beattie, before spells at Leeds, Wigan, Preston, Nottingham Forest and Oldham.
He returned to Blackpool and had a loan spell at Rochdale before two seasons with Wrexham.
Ormerod is currently looking for a club and welcomed the chance to link up with his old side to build up fitness.
A deal to rejoin Stanley has not been discussed at this stage, with the Reds already having a number of players under contract for the new season, but both parties are likely to assess the situation in the days to come.
More players linked up with Stanley for the first day of pre-season – including goalkeeper Cameron Belford, who had a loan spell with the Reds during the 2012/13 campaign and is now a free agent after leaving Tamworth.
Stanley’s contracted players were also present, with Michael Liddle, George Bowerman, Marcus Carver, Dean Winnard, Josh Windass, Will Hatfield and James Gray all recently signing new deals with the club.
The likes of Luke Joyce, Nicky Hunt, Piero Mingoia, Kal Naismith, Rob Atkinson and Tom Aldred were already under contract, while James Jenkins, Luke Greaves and Liam Goulding also join the first-team squad this season after signing professional deals to progress from the youth team.