Gallas is our primary target, says Redknapp

Harry Redknapp believes that "two or three" additions to his Tottenham Hotspur squad will put them in a position to finish above Arsenal next May, or even challenge for the Premier League title.

And he admitted yesterday that one of his targets is William Gallas, the former Arsenal captain.

Craig Bellamy of Manchester City and Scott Parker of West Ham United are believed to be two of the other names on Redknapp's shortlist of four, which was reduced from five when Joe Cole decided to join Liverpool. "They're the same ones I wanted from the start," he said. "If I can't get them I won't bring anyone in. They're not big money, in terms of transfers or anything. If I can get three of them, fantastic. Two, then great."

City are reluctant to let Bellamy go to a rival for a top-four finish, and Redknapp conceded that Fulham, managed by Mark Hughes, Bellamy's former boss with City and Wales, is a more likely destination. Parker has been offered a new contract by West Ham, although he has yet to sign it. But Gallas's contract with Arsenal expired at the end of last season so the only obstacles are the player's demands.

"He has not been greedy at all," Redknapp said. "His people have rung up and we spoke about it. I think he would be a good player for us. He has played at the top level, he won championships with Chelsea." But the Arsenal connection? "He played for Chelsea as well," Redknapp said. "If he comes in and plays rubbish then the crowd will slaughter him. If he comes in and plays great they will love him."

Tottenham's advantage in attracting players this summer is being able to offer Champions League football, and Redknapp intends to make it count. "We were behind Arsenal by miles for years and years but now we've got a chance to really push them and get above them. That would be great for Tottenham fans, and it's possible – we just need to improve that little bit now."

And his ambitions do not stop there. "I will talk to the players about winning the title," he said. "We will give it our best shot. Tottenham's never going to get a better chance and if you stand still and don't push on, others will pass you." Even with the distraction of Europe? "The Champions League's right up there in terms of priorities. You don't get many chances to be in it, so we'll be going for it as much as we can."

While Spurs fans lie down in a darkened room to calm their racing pulses after such a rallying cry, rivals will be sceptical about talk of a title. "I think we could be close," Redknapp insisted. "You need players who've won things and been around the place. Getting them is not easy but we'll see what happens.

"We threw some stupid games away last year – everyone did. Arsenal looked as if they could win it with seven games to go and if Robin van Persie hadn't missed most of the season you wonder what they could've done. I think Arsenal will be close this year, Liverpool will be close as well."

And, of course, he rates City, who visit White Hart Lane today. A second summer of heavy investment means that City will start the season under more pressure than any team, and may need time to bed their new players in, but Redknapp is not expecting either factor to weigh too heavily: "They were only just outside the top four last year and they've improved a lot and their manager [Roberto Mancini] has won championships in Italy, so it's not like they've just brought some novice in."

And he could easily field two teams of Premier League strength. "So long as he only puts one out, we've got a chance," Redknapp quipped. "I think they will be champions in the next three or four years, but there's no reason why we can't beat them."