
David Moyes has been monitoring Podolski's situation since Euro 2008 amid whispers that he is unhappy at Bayern Munich.
Podolski, 23, has confirmed he will be leaving the German giants by handing in a transfer request.
That has alerted a string of Premier League clubs - but it is Everton who plan to be first out of the traps.
Boss Moyes suggested last week that he will have little or no money to spend in the transfer window. But he is concerned about his striking options and the club are considering ways of raising the finance.
Podolski would not come cheap - but in the current climate, he is unlikely to be over- priced, either. A bid of just under £10million should be sufficient.
Moyes insists he will NOT sell to raise funds. But he may be forced to reassess the situation as problems mount up front.
New boy Louis Saha complained of a hamstring problem after the defeat at Wigan and James Vaughan, whose career has been plagued by injury, is going under the knife again.
Moyes' main asset, Yakubu, has had an indifferent start to the season.
Despite being a success at the European Championships - the Polish-born striker scored three times - Podolski has not been a regular at the Allianz Arena.
Spurs were interested in him but Harry Redknapp's priorities now lie elsewhere.
Manchester City have checked out Podolski but their transfer window targets are expected to be even more ambitious.
Moyes, meanwhile, believes that homegrown coaches are finally starting to get their chance.
He said: "Tony Adams, Roy Keane, Steve Bruce, Mark Hughes, Gareth Southgate and Paul Ince are the signs that this is happening.
"Arsene Wenger and Jose Mourinho have been fantastic for football in this country but other big names have come here and it hasn't worked for them.
"But Harry Redknapp's impact at Spurs will give a lot of chairmen reason to think going abroad isn't always the answer."
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