The Republic will take on Switzerland and Slovakia in Euro 2016 warm-ups.
Wolves defender Doherty comes into a 40-man provisional panel along with Aberdeen's Hayes and Peterborough midfielder Forrester.
"I want to give players a chance to impress," said Republic manager Martin O'Neill.
O'Neill's side face Switzerland on 25 March before a meeting with Slovakia four days later.
The squad, which also includes uncapped Brentford midfielder Alan Judge, will be shortened ahead of assembling on 20 March.
"The countdown to Euro 2016 starts now - both myself and my staff have been incredibly busy since qualification last November scouting and monitoring as many players as possible," added O'Neill.
"I know that I will have a very tough decision to name a final squad for Euro 2016."
Republic of Ireland squad:
Goalkeepers
Darren Randolph (West Ham United), David Forde (Millwall), Keiren Westwood (Sheffield Wednesday),  Rob Elliot (Newcastle United)
Defenders
Cyrus Christie (Derby County), Seamus Coleman (Everton), Richard Keogh (Derby County), John O'Shea (Sunderland), Alex Pearce (Bristol City), Shane Duffy (Blackburn Rovers), Ciaran Clark (Aston Villa), Paul McShane (Reading), Stephen Ward (Burnley), Greg Cunningham (Preston North End), Matt Doherty (Wolverhampton Wanderers)
Midfielders
Robbie Brady (Norwich City), James McCarthy (Everton), Jeff Hendrick (Derby County), Darron Gibson (Everton), Harry Arter (Bournemouth), Eunan O'Kane (Bournemouth), Glenn Whelan (Stoke City), Paul Green (Rotherham United), Stephen Gleeson (Birmingham City), David Meyler (Hull City), Stephen Quinn (Reading), Aiden McGeady (Sheffield Wednesday), James McClean (West Bromwich Albion), Alan Judge (Brentford), Jonathan Hayes (Aberdeen), Chris Forrester (Peterborough United), Anthony Pilkington (Cardiff City), Jonathan Walters (Stoke City), Wes Hoolahan (Norwich City)
Forwards
Robbie Keane (LA Galaxy), Shane Long (Southampton), Daryl Murphy (Ipswich Town), Kevin Doyle (Colorado Rapids), Anthony Stokes (Hibernian), Simon Cox (Reading)
Matt Doherty, Jonathan Hayes and Chris Forrester have received their first Republic of Ireland call-ups for two Dublin friendlies later this month.