Premier, the maker of Mr Kipling cakes and Bisto gravy, this week revealed it had rejected two bids from McCormick.
McCormick said in a statement on Thursday that it was now "willing to consider increasing its latest offer".
Meanwhile Japanese noodle maker Nissin Foods has agreed to buy a 17.27% stake in Premier Foods.
Nissin, which Premier describes as a "long-term shareholder", is expected to take a seat on the Premier board.
McCormick, known for its Schwartz spices and Lawry's seasonings, first made a bid of 52p a share last month and then raised it to 60p a share on 14 March.
Premier rejected it "on the basis that it significantly undervalued the company and its prospects".
Now McCormick has said it may be prepared to increase its offer following "limited confirmatory due diligence", i.e. a review of Premier's pensions documentation, current trading and material contracts.
McCormick said "it would be an outstanding custodian for the Premier Foods brands and, can provide benefits for Premier Foods, its pensioners, creditors and other stakeholders, which Premier Foods' current capital structure cannot deliver."
Some shareholders are keen for Premier to seek a higher offer.
David Cumming, head of equities at Standard Life Investments, the fund arm of insurer Standard Life, which controls 7% of Premier, said: "Although we believe the 60p  bid indicated by McCormick is too low, we remain open to a bid at a higher level.
"We expect the Premier Foods Board, on behalf of its shareholders, to engage with McCormick and pursue this option to the full."
Premier shares have been on a roller coaster ride this week, soaring 50% on Wednesday following news of the McCormick bid, falling by more than 10% on Thursday on the announcement of the Nissin stake and then recouping nearly all their losses as McCormick said it might be prepared to pay more.
Premier used to be one of the UK's biggest food groups but came unstuck when it expanded too fast, loading itself with debt.
It has since sold off its Hovis bread business to the US-based Gores group, rebuilt its £20m production line at its Mr Kipling bakery in Barnsley and pushed through a £1.1bn refinancing package, which included a £353m rights issue.
It still owns a range of household UK brands such as Ambrosia rice pudding, Oxo stock cubes and Batchelors soups.
Premier is increasing its international operations following a recent co-operation deal with Nissin that allows Premier to distribute its products in the UK, while making its own products more widely available in key overseas markets.
Nissin invented the first instant noodles in 1958 and operates in 19 countries. Its products include Cup Noodles and Top Ramen.

Zoo staff cared for the injured bird and it is being returned to its owner in south Wales.
'The Pit Man' had failed to return from a race in the south of France five weeks ago.
Owner Craig Dewar, from Abertillery, Blaenau Gwent, said he was "thrilled" his bird had been found.
Zoo worker Justin Aird said: "I was just giving a public talk about how the meerkats stand sentry duty to look out for birds of prey when suddenly there was a commotion overhead. Moments later, the pigeon dropped out of the sky and landed nearby."
Staff found the bird's identity tag and contacted Mr Dewar.
Zoo curator Colin Northcott said: "Obviously the bird was very shaken and had sustained some minor injuries but he was very lucky to have fallen where he did.
"If it had been anywhere else, even in a more remote part of the zoo, the buzzard would surely have finished him off."
The bird got its name as it always flies home over the site of the former Six Bells Colliery in Abertillery.
Mr Dewar said: "I was thrilled to hear that he'd been recovered. I just can't believe that he will be back with us soon."
The Pit Man will be able to give his wings a rest on the journey home as he will be couriered back by a specialist.
McCormick, the American food flavourings business, has said it may increase its $700m (£494m) bid for the UK's Premier Foods.
[NEXT_CONCEPT]
A racing pigeon feared lost has turned up after plummeting out of the sky into Dartmoor Zoo in Devon following an attack by a bird of prey.