The Greek club have money to spend and have identified Pogatetz as the ideal candidate to slot into the heart of their defence.
Strachan thought to have held talks with the agent of Rangers striker Kris Boyd yesterday will do his best to resist their overtures, but with limited cash available to spend this month it could come down to how much Panathinaikos are willing to offer.
An interesting twist is that Pogatetz is out of contract in the summer and free to talk over an end of season move now, when he could turn his back on Middlesbrough for nothing if he receives a better offer.
Such a situation could mean Strachan being forced to listen to offers this month, knowing any funds received would also increase his own transfer budget.
Panathanaikos have been knocked back in their attempts to sign Italian defender Marco Materazzi, but recently appointed coach Nikos Nioplias has turned his attentions towards Pogatetz and Boca Juniors defender Gabriel Paletta.
Athens-based sources claim Panathanaikos are willing to offer the defender around 1.1m euros a year, tax free at the end of his current contract, which is likely to equate to marginally more than he is earning at the Riverside.
But the Superleague leaders are putting their proposals together and director of football Kostas Antoniou will try to test Middlesbrough into selling on the cheap this month.
Strachan has money available and he has been in Scotland in the hope of making progress on incoming transfers.
He still hopes to have made signings before sixth-place Swansea arrive on Teesside this Saturday, although hopes of that happening are fading.
Celtic are reluctant to move on defender Gary Caldwell, midfielder Barry Robson and striker Scott McDonald for less than their valuations or until they have lined up replacements.
With Bhoys boss Tony Mowbray yet to make significant progress himself on the transfer front, Strachan might have to remain patient. He was also linked yesterday with a move for Celtic's out of favour targetman Chris Killen.
Strachan was at Celtic Park on Sunday to watch his former club draw with Rangers 1-1 and he is understood to have held talks with the agent of Boyd 24 hours later.
Rangers are loath to lose Boyd, out of contract in the summer, but their financial situation could force them into accepting a low offer.
Strachan faces competition for Boyd, with clubs from the English Premier League and abroad also interested.
Birmingham and French outfit Sochaux have been monitoring his position, but Strachan hopes the promise of leading Middlesbrough's promotion drive will help lure him to Teesside.
Rangers are expected to hold talks with Boyd's representative Mark Donaghy this week.
But with Rangers determined to do all they can to keep him until the end of the season at least, Strachan knows he could be forced into a rethink.
The Middlesbrough boss still looks favourite to land Boyd's Old Firm rival Caldwell, after the former Newcastle defender was told to forget about having his pay demands met at Parkhead.
It has been suggested in Scotland that Middlesbrough are trying to sign the player for £350,000, just a few weeks after it was claimed Celtic wanted £1.5m for the defender and team-mate Robson.
Middlesbrough appear to be close to offloading one player this month, with Mohamed Shawky in talks to leave.
Shawky's agent Nader Shawki said: We have an offer from a top club in Turkey. I will be there to conclude negotiations on Monday.
Boro, meanwhile, have confirmed that left-back Andrew Taylor will undergo a double hernia operation today, having put off surgery during Strachan's injury crisis.
Boro's reserve game at Rotherham tonight has been postponed due to a frozen pitch tonight.