Hartley and Vennegoor of Hesselink are both out of contract at Celtic
Celtic have confirmed the departures of striker Jan Vennegoor of Hesselink and midfielder Paul Hartley.
Manager Tony Mowbray said: "I had a good long conversation with Paul. He came in to see me.
"The outcome of that is Paul won't be offered a new contract. He is free to look for other employment.
"I have had no contact with Jan. Jan is out of contract - he is free to seek other employment and I'm pretty sure that's what he will be doing."
Hartley is poised to make a decision over his own future having been offered a contract by Greek top-flight club Iraklis Saloniki.
Hearts were also interested in bringing the 32-year-old Scotland international back for a second spell at Tynecastle.
Hartley, who started his career with Hamilton and also had spells with Millwall, Raith Rovers, Hibernian and St Johnstone, had been with Celtic since 2007.
Netherlands international Vennegoor of Hesselink has been linked with moves back to his homeland.
Hopefully we will make one or two signings the supporters get excited about
Celtic manager Tony Mowbray
The 30-year-old striker, who spent three seasons with Celtic, previously played for FC Twente and PSV Eindhoven.
Mowbray is hopeful of making Nancy striker Marc Antoine Fortune his first signing and others to his squad.
"I want to put my own stamp on it, bring some players in that I want to bring and have attributes that I like in footballers," he said.
There is some sense of urgency in Mowbray's quest given that Celtic begin their Champions League qualifying campaign on 28 or 29 July.
"We would like to get one or two in before that," Mowbray admitted.
"We're working very, very hard. It's not always easy, especially when you're looking for good players with options.
"Hopefully we will make one or two signings the supporters get excited about.
"Hopefully they will be of the right standard to lift the quality and intensity on the training ground."
Mowbray, who is unsure whether Scott Brown and Stephen McManus will recover from injury in time to make the European kick-off, recognises the need to be imaginative in the transfer market though.
"You can find some very, very talented individuals that you can get cheaper," the former Middlesbrough captain said.
"We tried to do that at Hibernian and I like to think we proved that you can do that.
"The expectations sometimes of the bigger clubs is that they want ready-made footballers.
"My job I feel is to try to give them some ready-made footballers but also to build this squad and find some players that our supporters will never have heard of and yet become big players. It's about getting the balance."
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