Mark Warburton's Rangers kicked off their league season by drawing 1-1 at home to Hamilton on Saturday, while Brendan Rodgers's Celtic beat Hearts 2-1 on Sunday courtesy a late winner from new signing Scott Sinclair.
Warburton, whose Rangers side won the Championship by 11 points last term, has signed nine new players this summer in a strong recruitment drive which has strengthened claims that they ought to compete with their Old Firm rivals.
However, they have relied on shrewd free transfers and paying modest compensation fees for the talent they have signed this summer. Nevertheless, King expects the 53-year-old manager to compete with Rodgers on the domestic front with the players he has signed.
“The resources Celtic have at this point in time are clearly very, very substantial relative to ours, in terms of the footballing side," he told The Scottish Sun.
“But Celtic have resources to compete in Europe. That is really what they are there to do. We are not competing in Europe this season so our standard this year is that we expect to compete with Celtic.
“Last season, I said the non-negotiable was winning the Championship. I would say this year we should at least come second.”
Of course, Celtic are already two points clear of Rangers in the table, but it is a long, long season and nothing is won after the first week of the campaign.
Rangers fans will also be wanting a serious challenge as they bid to deny Celtic a sixth successive title.