City council leader Colin Glover said the authority was aware of stores showing interest because of the arrival of the discount fashion chain.
David Jackson, commercial director of The Lanes shopping centre, where Primark is due to open in October, confirmed that two other fashion retailers – described as “decent” names with stores in Glasgow and Newcastle – are likely to follow its arrival.
Mr Glover said: “There’s a real confidence in the city. It’s really good to see that positivity and confidence at a time when people are generally a bit nervous of investing.
“We are already aware of people showing interest because of Primark coming. But it’s not just about shopping. It’s also about cafés, restaurants and the heritage of the city.
“That’s the journey we are on and there’s a really good vibe in the city.”
Mr Jackson told in-Cumbria.com he hoped that one of the retailers would open before Christmas and the other in the new year. He also said two new accessories shops were interested in coming to the Lanes.
He said: “I can’t name names as deals have not yet been finalised but the clothes shops are decent retailers. You will find these stores in Newcastle and Glasgow.
“The accessories stores are also good. One of the clothes shops that is coming knew about the Primark deal being on the table.
“Primark will bring a lot more people into the city. Retailers are attracted by the opportunity.”
Jobs are being advertised at Primark, which is being fitted out.
The retailer is taking over the former BHS store, which closed in January. It has signed a 25-year lease.
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