Phelan had only 13 first-team players available for Hull's first game against defending champions Leicester City, but the team managed to pull a rabbit out of the hat with a 2-1 win at home, before beating Swansea City away 2-0 a week later.
The club's winning run ended with a 1-0 defeat by Manchester United on Saturday, prompting Phelan to renew his calls for strengthening the squad before it was too late.
"We have to sit down, me and the owners, sometime. Now we have no game, it is vitally important we do it," Phelan told reporters. "We are active but at the moment nothing has been concluded. We need to get cracking.
"I think it is a year since we have signed an outfield player. These players here need help. We need to make news. It is going to be touch and go.
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"The players deserve some more quality to come into the club. They deserve a break. Everything is in place to do some business.
"The recruitment staff and coaching staff have worked very, very hard and we just need to get those deals done — the sooner, the better."
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
