Sixteen animals were killed at the Bewdley attraction after a pack of African wild dogs escaped from their compound due to damage caused by Storm Ciara.
Staff were left "extremely saddened" by the loss of six deer and 10 sheep last weekend.
The safari park had been due to reopen on Saturday for the new season in time for the school half term holiday next week.
But despite the sadness over the deaths, the park says it is planning to open as normal this weekend.
The storm is likely to bring substantial rainfall, but gusts are expected to be less damaging than during last weekend’s Storm Ciara.
A spokesman said: “We currently have no plans for West Midland Safari Park to be closed during the weekend.
“However, we assess conditions on a daily basis and make our own judgement, based on the circumstances of the park and always in the best interests of our animals and public safety.
“We are aware of the current weather warnings with Storm Dennis and will monitor this closely.”
A spokeswoman for the park said 12 wild dogs were able to enter a neighbouring compound in the early hours of February 9 as the storm hit the country.
The compound housed Persian fallow deer and Barbary sheep.
"At no point was there a risk to public safety and there was no danger of any animals escaping the park's perimeter fencing," the spokeswoman said.
She said the wilds dogs were returned to their compound unharmed.
"The wild dogs entered the neighbouring compound through a gated entrance which had been damaged in the storm which hit Worcestershire earlier that morning," the spokeswoman explained.
She added: "Given their personal attachment to our animals, our staff are extremely saddened by the incident."
Commenting on the impending arrival of Storm Dennis on Saturday, the spokeswoman said: "We are aware of the current weather warnings in place for this weekend and will monitor this closely, making our decisions, as always, in the best interests of our animals and public safety."
According to the World Wildlife Fund (WWF), the African wild dog is "one of the world's most endangered mammals", with only about 1,400 left in the wild.
The largest populations remain in southern Africa and the southern part of East Africa.
The predator, which gathers in packs, hunts species such as gazelles and can reach speeds of more than 44mph.