The Yorkshire chief executive made his claim after the success of last week’s match between England and West Indies.
Both in cricketing and commercial terms, the game was a triumph, West Indies winning a thrilling fixture by five wickets with 4.4 overs left, watched by an aggregate attendance of 56,005.
Arthur admitted that Headingley is not among the top four grounds at present, saying it is for others to determine where it presently sits in the pecking order, but he believes that the target is achievable.
“Our desire is to be one of the top four international cricket grounds in England,” he told The Yorkshire Post.
“We are outside the top four at this moment in time, and we won’t be inside it, however well we operate, until our new main stand is ready in 2019.
“The two ingredients that we’re missing at the moment are the new main stand and the allocation of a regular summer Test match.
“Hopefully, as a result of last week, Headingley will once again be invited to the top table of international cricket in this country, and the ground will go from strength to strength.”
No dispassionate assessment of England’s Test stadia could fail to advocate such as Lord’s, Trent Bridge, The Oval and Edgbaston for inclusion in any hypothetical top four.
Headingley has plenty of competition in the increasing clamour to stage international games, but the new stand will raise its capacity from 15,500 to 18,350, while the ground traditionally throws up compelling cricket.
“We will find out in February who will be allocated international matches from the years 2020 to 2023, and last week’s match can only help our cause,” added Arthur.
“We priced the game sensibly, we marketed it well, and in recent times we’ve improved access to the ground and we’ve improved the environment within the ground.
“Ticket sales were £200,000 up on last year’s Test, and it’s a place where you always seem to get exciting cricket.
“We’ve got a magnificent team here at Headingley, who are all totally motivated and who buy into the vision of Headingley going forward.”
Vital to the success of last week’s game was its favourable position in the calendar; it took place over a Bank Holiday weekend and was blessed, for the most part, with glorious weather.
The previous four Headingley Tests were early-season affairs, three of them starting in May, and against England’s lesser opponents of the summer in often unfavourable conditions.
Yorkshire are expected to have another May Test next year against Pakistan before Australia visit in 2019 for the first Headingley Ashes Test since 2009.
After that, the old system whereby the England and Wales Cricket made cash-strapped counties bid for games is being changed, signalling an end, hopes Arthur, to Test matches in northern England in May.
“We’ve just had a summer Test at long last, which is very important,” he said. “In the north of the country, the Tests should take place in the last week of July and during August, when the weather is traditionally much better.
“We shouldn’t have to endure a late May or June Test match in this part of the country, as it’s unfair on the people that live in this area. I’m not just talking about Headingley, but Old Trafford as well.”
Arthur believes that Test cricket is not just about money but about engaging with communities and making sure that spectators are treated fairly.
He believes that Yorkshire’s commitment to this was reflected in ticket prices for last week’s match.
“Not only did we price it realistically, but we also recognise that people who live in this part of the world cannot afford the prices that they can afford in London, and that has to be recognised by cricket,” he said.
“Next year, for the Pakistan Test at Headingley, there will be adult seats from day one priced at £20, even though it’s a smaller capacity because of the loss of the main stand.
“This year, although West Indies, on paper, weren’t the most attractive of teams, we pre-sold a lot of tickets and the public responded as the match unfolded.
“Because West Indies performed so well, we actually sold 3,000 tickets online overnight before the final day, so pricing is very important.”
Another key factor to the success of any Test match is the pitch. The surface at Headingley was widely praised, with Arthur adding his own words of appreciation.
“The pitch that Andy Fogarty and his team produced was outstanding for Test cricket,” he said.
“His pitches all season have been appropriate for the type of cricket that we’ve been playing, be that one-day, four-day or five-day cricket.”