The agent of in-demand Benfica striker Oscar Cardozo claims his client would be happy to remain in Portugal.
Reports have linked the Paraguay international with a move to the Premier League, with Manchester City and Cardiff City said to be among those keen on doing a deal.
Quotes attributed to Bluebirds boss Malky Mackay over the weekend suggested that he was planning a big-money bid.
Cardiff have, however, moved to distance themselves from an audacious approach, and Cardozo's representative admits no agreement is close.
Pedro Aldave has also suggested that the prolific 30-year-old old could now end up staying put, having previously hinted that a summer transfer was all but wrapped up.
He told Diario de Noticias: "Is he certain to join Cardiff next season? I am not aware of such information.
"Cardozo will be in Lisbon on 17th July to start pre-season training at Benfica, where he wants to stay."
Starnes will depart Huish Park at the end of this week after almost six years with the Somerset club, culminating in May's promotion to the Championship via the League One play-off final at Wembley.
The 58-year-old, formerly chief exec at Swindon, will also join the board at Plymouth when he starts his new role on Monday.
Argyle chairman James Brent told the club's official website: "My fellow directors and I are delighted to welcome Martyn to Plymouth Argyle.
"Martyn brings years of experience in running football clubs and has demonstrated that, even for a club which has a much smaller fanbase than Argyle, financial prudence can be combined with league success.
"We are confident that Martyn will leverage the additional revenues anticipated from the new grandstand to support John Sheridan in moving Argyle back up the Football League. It is a measure of Martyn's confidence in Argyle that he has decided to join us from a newly promoted Championship club.
"I look forward to the new season with enthusiasm and excitement."
Meanwhile, Yeovil have also wished Starnes well in his new role.
Town's official website read: "All the staff and board of directors would like to put on record their thanks to Mr Starnes for all his work for the club during his time at Huish Park, and wish him the best of luck at Home Park in the future."
Veteran midfielder Oakley was not offered fresh terms at the end of last season due to the club's delicate financial situation but Tisdale has always stressed his desire to try and hang on to the 35-year-old.
Defender Tully, meanwhile, was one of a handful of players offered a new deal although he is yet to sign and the offer has had to be put to one side for the time being, with Tisdale now unsure whether the required funds are still available for the right-back.
The Grecians boss told the club's official website: "Matt Oakley hasn't signed yet, but he's come back to training and he wants to play for us. We've been very transparent over the last month or two that we'd like to sign him and we'll try to find a way.
"In very tough times, the club have been doing all they can to make it possible for me - so I'm hoping that will get done."
Regarding Tully, he added: "The club is doing everything they can to make funds available for me, but there's no guarantee that I'll be able to make that signing.
"Steve was in training with us Monday and he's not yet signed elsewhere, so it'd be great if I could keep hold of him - but that's the way things are. It's a 'wait and see' on that one, but there's no guarantee that I'm going to be able to do it."
Meanwhile, highly-regarded midfielder David Wheeler has joined Exeter on trial from non-league Staines this week with the hope of impressing Tisdale.
The 20-year-old only arrived at Valley Parade last summer following a successful trial but proved to be a valuable member of manager Phil Parkinson's side during his debut campaign.
McHugh made 28 appearances in total including six Capital One Cup starts as he helped the Bantams reach a memorable Wembley final, even getting his name on the scoresheet in a dramatic 3-1 semi-final first leg victory over Aston Villa.
McHugh's efforts for Bradford last term saw him recognised at Under-21 level for the Republic of Ireland.
He will now look to establish himself as a regular starter in Parkinson's XI as the Bantams aim to survive in League One following May's play-off success.
