The manager recognises the Merseysiders and Bobby Robson's Newcastle United as big clubs alongside us on their way back from darker days - and sees potential in one of them to break into the current big five in the Premiership.
Certainly Everton's recent history mirrors ours. They missed out on relegation by just two points in 1996-97 and in 1997-98 were battling with us to avoid the drop - this time they managed it by the skin of their teeth on goal difference.
Super-successful at Glasgow Rangers, Walter Smith, pictured right, arrived at Goodison Park in July 1998 and has started to turn things around with Toffees finishing mid-table in the last two seasons. Now he is looking to take the next step.
Graham said: "If you think of Everton just a couple of years ago they were struggling to avoid relegation, a bit similar to Spurs. Both are big clubs, both have fantastic potential and Walter Smith has now gone in there, steadied the ship, moved them away from relegation problems and they've finished mid-table in the last two seasons.
"I'm sure their fans and Walter will look to take it to the next step now, again like us. We're big clubs with full-capacity gates, good potential and now we have to try and break into that top six."
After a win, draw and loss in our first three Premiership outings, the boss is now looking to capitalise on successive home games against Everton on Tuesday and the televised derby against West Ham next Monday.
He added: "It doesn't always work out the way you plan it but we've two home matches now and it would be nice to think if you get six points you would be in a lovely position."
George Graham can seen more than a few similarities between ourselves and Tuesday night's opponents Everton.