The three players are currently competing for two front-line positions at White Hart Lane and the early evidence is that the rivalry is paying dividends for Spurs.
Graham is still an admirer of Sutton, who he tried to sign for Arsenal from Norwich four years ago, but lost out to Blackburn. Rovers paid pounds 5m for Sutton and made him one of the best-paid players in the Premiership but now could be tempted to sell if they sign the Coventry striker Dion Dublin.
However, Graham has indicated he is prepared to delay any move into the transfer market until all his current squad have been given the chance to fully demonstrate their abilities. Midfield and defence are believed to be the key areas Graham will address first but he said: "I'm delighted with the response I've had from all the players in the few weeks I've been here.
"It seems obvious that we will eventually have to add to the squad, because Spurs only just avoided relegation last season and it is the same players still here.
"But there is not much top quality available on the market at the moment wherever you look and until the right player crops up I will work with the players we have here and get the best out of them."
David Pleat, Tottenham's director of football, tried to sign the midfielder Tim Sherwood from Blackburn before Graham arrived at Spurs from Leeds and there was speculation then that Sutton was also a transfer target. However, Spurs' pounds 3m bid for Sherwood was rejected by the Rovers manager, Roy Hodgson.
Pleat said yesterday: "Since then there has been no further contact with Blackburn and Sutton's name has never featured in our negotiations."
Tottenham showed the spirit and character Graham demands with a 3-1 win at Northampton on Tuesday night in the Worthington Cup when the slippery, rain-sodden conditions presented just as much of a test for them as the Second Division side.
Graham was saved a selection dilemma by Ferdinand's unavailability with an ankle injury and Armstrong scored twice, in partnership with Iversen, to ease Spurs' passage through to the last 16 after Sean Parrish opened the scoring for Northampton.
Iversen had a quiet game but the former Rosenborg striker has already scored three times this season as a substitute, including both goals in last Saturday's 2-0 win over Newcastle, and Graham has predicted a secure future for him at White Hart Lane.
If Sutton arrived at Spurs it would be seen as a setback for Armstrong, who believes he is back near his best form this season after nearly two years battling against an ankle injury which took three operations to repair.
He said: "Last season I came back and had a few games but in the end it was obvious I was playing without being properly fit.
"In the last few games, though, I have felt a lot sharper and I'm confident that, finally, I'm getting very close to 100 per cent again. All I want to do now is keep my place with Spurs and put the injury situation behind me."
David Ginola, who many believed would not fit into Graham's plans for Tottenham because of his flamboyant temperament, again showed at Northampton that he can produce outstanding skill, even in the worst conditions. But he is out of Tottenham's next match, at home to Charlton on Monday, when he will serve a one-match suspension after being booked five times this season. That total rose to six when he was shown another yellow card in Saturday's win over Newcastle.