Goodwin feels St Mirren's style of play was crucial in tying up the 24-year-old Scotland striker and he hopes the same reason can help in getting Jake Doyle-Hayes to extend his stay.
Kilmarnock manager Alex Dyer wants Brophy to move this month after the forward pledged his long-term future to Scottish Premiership rivals.
Goodwin said: "It's something we would love to do and will try to make it happen but at the moment he's a Kilmarnock player.
"He was one we asked about last January when Kirk Broadfoot went the other way. This time round we are delighted to get him on a pre-contract. I have got to congratulate the board and (chief executive) Tony Fitzpatrick on getting it done.
"Players of quality are always in demand from teams in England and Scotland and there were a number of clubs interested in him. The number of messages I got from coaches of other teams to say what a fantastic signing it was...
"He is a brilliant age and he is hungry and ambitious. He wants to come here, score as many goals as possible and get in the mind of Steve Clarke, the national coach, and hopefully to kick on to bigger and better things.
"He has watched us on a few occasions and likes the way we are trying to play. Eamonn is suited to a certain type of football and that's probably the reason why he is not playing for Kilmarnock at the moment, because Alex Dyer likes to play a 6ft 3in target man.
"We are not playing that way. I see Eamonn as being a number nine but not one who is going to have to go and win flick-ons."
Goodwin added: "We are blessed here at St Mirren with fantastic training facilities and a brilliant grass pitch.
"Eamonn has worked only on plastic pitches during his time at Hamilton and Kilmarnock so I'm sure that will be a huge attraction to him, coming here and playing on a decent surface.
"I think he can see how ambitious we are and the progress we are making and he wants to be a part of it."
Goodwin added that 22-year-old former Aston Villa midfielder Doyle-Hayes was "mulling over" a "really good" contract extension offer.
The Republic of Ireland Under-21 international has made a big impression since joining Saints in November and is contracted for the rest of the season.
"There's competition for any good player, especially someone of the calibre of Jake but I have had good conversations with Jake," Goodwin said.
"The reason Jake is attracting the interest and getting the plaudits is because of the way our team plays and the way he fits into it.
"Jake is no use going to a team that plays back to front quickly. We like to involve the midfielders and Jake is pivotal to that.
"I do believe if he stays here for another year to 18 months then there's a lot to come from him and he will have even bigger and better offers on the table than those that are there just now."