The union has been in dispute with the organisation since November, when the charity announced plans to sack its entire workforce and re-employ staff on new contracts in a bid to cuts costs.
Unite said the charity’s 2,300 employees were presented with new contracts last Monday, which they must sign by 17 May or risk losing their jobs.
It said that the new contracts offered to staff had inferior terms and conditions and could leave some staff out of pocket by as much as £10,000 a year.
And it claimed that staff were being prevented from signing the contracts "under protest", which the union said would limit their ability to subsequently take legal action.
Turning Point said that it would not allow employees to sign under protest, but this would not prevent them from taking legal action.
Unite said it would hold a consultative ballot by the end of the week with its more than 600 members at Turning Point to gauge whether they would be prepared to take strike action over the new contract.
Jamie Major, regional officer at Unite, said the charity had employed "bully-boy tactics" to limit its employees’ legal freedom by including a clause in the new contract that would prevent them from signing under protest. "They are attempting to stop their employees exercising their legal right," he said.
Major said employees had the legal right to sign contracts they are unhappy with under protest and then claim breach of contract. If a breach of contract claim is successful it could result in the employee being awarded compensation, or even force the employer to reinstate the original contract, said Major.
He said that Turning Point had also failed to give its employees the legally required three months’ notice of a new contract – it announced on Monday that staff had until 17 May to sign the contracts, giving a notice period of less than 10 weeks.
If Turning Point employees fail to sign the contracts, or sign under protest, they will lose their jobs, he said.
"Turning Point is an organisation that’s growing," said Major. "If you look at its accounts, it’s growing; it is not an organisation in crisis. It wants to expand to compete with its competitors and it is taking more than £2m out of the pockets of staff to do it."
A spokeswoman for Turning Point said it was not accepting any contracts signed under protest to ensure that the signed contracts were valid and effective.
"The ability to claim unfair dismissal is not at all compromised by this and remains an individual’s statutory right," she said. "We have exceeded the legal and contractual notice period and this is also not compromised by asking staff to sign by 17 May.
"This timeframe is intended to give us enough time to put in place any contingencies so that we are able to ensure our service users continue to receive the care and support they need."
Unite will issue a consultative ballot this week asking members if they would consider taking industrial action up to and including strike action. The outcome of the ballot will be known in two weeks and, if responses favour action, members will then be balloted again.
After the second ballot, strike action could take place within a month, Major said.