Arsenal's midfielder Jack Wilshere has warned Manchester United that his team are increasingly convinced they can overtake the leaders at the top of the Premier League table.

United were the only one of the top five teams to win this week and results left them with a two-point lead at the summit and four points ahead of Arsenal with a game in hand. However, far from being deflated by Arsenal's failure to find a way through the massed ranks of Manchester City during Wednesday's 0-0 draw between the sides in second and third place, Wilshere said that both City's approach and his own team's performance increased Arsenal players belief that they can be crowned the best team in the country. The 18-year-old indicated the club could take a giant step to fulfilling that ambition by beating United when they travel to the Emirates Stadium on 30 April.

"We showed [against City] we can dominate games," said Wilshere. "At the end of the day, we wanted a goal but it's a point and we look forward to catching United. I think they will be delighted with the results but they have still got to come here so its still really open. When they come here, we can beat them."

Wilshere conceded that in order to be in a position to ensure that victory over United in April would turn the title race in their favour Arsenal must improve in terms of converting possession in goals. For years Arsenal have been accused of lacking the penetration to go with their intricate interplay and that allegation was made against them again as City successfully kept them at bay for 90 minutes. Wilshere, however, said Arsenal are addressing that problem to ensure it will not hamper them during the title run-in.

"Teams come here and they defend and they are scared of us, we have to learn to break them down," said Wilshere. "We work on that in training and we showed it [against City] – we just missed that killer edge in the box. But it'll come – we will get the goals in games like that because we know that teams will come here and defend. We have got quality strikers here with Robin [Van Persie], [Marouane] Chamakh and Nicklas [Bedntner]– we'll get the goals."

Wilshere highlighted last month's 3-1 demolition of Chelsea as the result that proved that Arsenal can deliver when it counts and suggested that their confidence will soar even further if they end a five-year trophy drought by winning the Carling Cup at the end of February. Arsenal face Ipswich Town in the the first leg of semi-final next week.

"After the Chelsea game we all thought this could be our season," said Wilshere. "Now we think it's a new year and a new start and we are really going to push on. We are undefeated this year and hopefully we can keep going like that. I think the Carling Cup is massive because we want to win something and if we can win something in February, it will give us confidence for the rest of the season."