The 70-year-old Moores previously owned the San Diego Padres Major League Baseball franchise in California but sold the team for $800million in 2012 and it is understood the Texan is in negotiations about taking an equity stake in a club currently sixth in the Premier League.
Swansea survive mainly on television money and transfers and club chairman Huw Jenkins said last month that the club were "miles behind" most of their rivals in terms of commercial income and had to look at alternative revenue streams to compete in the top flight of English football.
Swansea City Supporters Trust, which owns 21 per cent of the club, remains wary of external investment and ownership change, but Monk says fans must trust a board which has taken the club from the bottom of League Two into the higher echelons of the Premier League and Europe in the past decade.
"It's important as a club that we look to push forward," Monk said at his press conference ahead of Saturday's league game at Everton.
"The way to do that is maybe attract other interest and other investment and there are areas of the club that need to be strengthened - facility-wise, commercially, infrastructure and expansion of the stadium.
"I know we've been talking about all these things, to be proactive and attract investment.
"But what I would say is over the last 10-11 years you speak to everyone who's been involved at this club and Huw and the board have always made the decisions with the best interests of the club in mind.
"Whatever happens in the future, as long as those guys are here they will do exactly the same.
"It's not about someone coming in and taking over everything, people should have trust in the board that they will do whatever's best for the good of Swansea."
Monk feels extra investment is essential to keep pace with the Premier League's biggest clubs, who he says will become even wealthier in the years to come.
"You get money for staying in the league but to take that next step you need extra investment and it's only going to get more," Monk said.
"The bigger clubs are going to stretch away with more money and the clubs that are left behind must try to stay on their heels enough to compete.
"This is a way of doing it and that's what the club is looking at.
"Of course I can understand the fans' concerns but Huw and the board are very shrewd in what they do.
"That will never change and I'm sure if someone ever comes in they will follow the line of what's been done before and that the control element will always be the structure we've had.
"So I don't think it's a worry for anyone."
Monk also spoke about his fiancee's anger after she received a letter which was apparently hand delivered to the couple's family home criticising his performance at the Liberty Stadium.
Lexy Blackwell, who gave birth to twin boys in March, posted on Twitter on Wednesday afternoon claiming she had received the letter from a neighbour and expressed her disgust at the incident.
She has subsequently deactivated her Twitter account and Monk said he had sympathy for his fiancee.
"Someone wanted to impart their wisdom on me how he would deal with matters in hand and the best way to go about it," Monk said.
"There was no malice about it but for my missus and kids when we're at home that's when football is left at the door.
"My property is where I spend my time with my kids and missus and for them not to be exposed to certain situations.
"My missus got the letter and she wasn't too happy that someone could come up and post it where she and my kids are and where we live.
"She felt a bit upset about it and vented her anger, and quite rightly so, but it's not a big issue.
"She's used to speaking her mind but I've told her that not everyone is going to write nice things on Twitter."
Source : PA
Source: PA