Thompson cited Championship ambition when he turned down a fresh Blues contract – yet is still to find a club.
Having left on good terms with Jackett, the 28-year-old has been allowed to bolster his fitness by training with his former employers.
It was a request from Thompson that Pompey’s boss was willing to grant.
Although, with Anton Walkes and James Bolton vying for the right-back spot, Jackett has stressed re-joining the club is not under consideration.
He said: ‘Nathan is somebody I have a lot of time for on a personal level and, if I can help him, I will.
‘Obviously, he is looking for a club, he has been to one or two places without signing but, on the days it suits us, he can come in for some general training.
‘He approached me. I spoke to him on Wednesday and asked how he was getting on and after that chat he welcomed training with us.
‘There isn’t anything permanent for him – we have Anton Walkes in the side at the moment and James Bolton nearing fitness with an ankle injury.
‘While I don't think James will make it this weekend, I would anticipate him training Monday or Tuesday and being fit for Sunderland.
‘You can have three right-backs in a squad, but it’s better to try to distribute it.
‘I always feel if you need extras it’s centre-forwards and goalkeepers, then after that there are certain positions where if you get an unusual amount of injuries other people can play – and right-back is one of them.
‘There are midfield players and others who can play that position, I do feel we are well covered.’
Thompson was Jackett’s first signing of his Pompey managerial career in June 2017.
The former Swindon defender went on to amass 78 appearances and one goal during his two Fratton Park seasons.
Jackett added: ‘I am happy to help. Obviously he is looking for a club, he is not dictated to by deadlines, windows or anything like that.
‘He's somebody I have a lot of time for, if I can help him with a few sessions towards his end goal – which is his next club – then I am happy to do that.’