It says redundancy notices will be withdrawn if the three unions agree to ballot their members on the pay offer.
The GMB union says there has been a drop in school meals quality since the service was outsourced.
Staff employed by sub-contractor Idverde are to strike after rejecting a 70p per hour pay rise.
Spokespeople for GMB Union and Unison say Brighton and Hove Museums staff have ended their dispute.
Unions are calling for a 20% pay increase but council-owned GYS says it cannot afford that demand.
A legal ruling means coastguard officers are now classed as employees, so new rules are planned.
Andy Burnham's possible chancellor could be among the conversations between unions and the prospective prime minister.
A volunteer from the Borders says plans to remove their remuneration has hit morale in the service.
Staff walked out due to concerns about an alleged "dangerous" crane lift, a union says.
