I thought there was 2 years of KG trade rumours before the deal happened. Boston was one of the teams mentioned but never a frontrunner. Boston was also linked with a bunch of other stars. Everyone knew Ainge was trying to swing for a big name. Iverson was a big one. Pau Gasol was another. I forget who else.
The two main teams in the KG chase were Phoenix and the LA Lakers. Phoenix were willing to deal Marion but were reluctant to deal Amare Stoudemire. Minnesota wanted Amare. So that deal never got made. LA were offering Odom and Andrew Bynum (hadn't broken out yet, only 7ppg 5rpg).
The other team that got mentioned a lot in trade deals was Chicago. The Baby Bulls had lots of trade assets and were getting mentioned in everything. I don't remember if they were in the KG chase but they probably were.
Boston, on the other hand, was a secondary option. They didn't have great trade assets. They had a lot of good pieces. Expiring deals. Good young players. Good draft picks. But no great pieces you could build a team around. So they couldn't get in any of the trade negotations for the top players and were instead looking for the 2nd tier guys (like Iverson or Pau) who weren't valued as highly.
That all changed in the season before the KG trade. Paul Pierce got hurt and missed almost half the season. The Celtics went from a near .500 team (20 wins, 27 losses) to the worst team in the league (7 wins, 31 losses) without Pierce. Suddenly Boston had a great chance at a top pick in a top draft (Durant, Oden).
The second thing that happened was Big Al broke out. He went from a 7ppg 5rpg bench big man to a 16ppg 11rpg who posted 20-11 after the All-Star break. Al Jefferson had announced himself as a future star in the making. The type of low post offensive weapon you could build your team around. Now Boston had 2 blue chip trade assets (Big Al, 2007 draft pick).
This changed everything and made Boston one of the frontrunners in the trade market. This is when Boston became one of the main options in the KG trade chase. Even then though, LAL and Phoenix were considered above Boston. However Phoenix were still unwilling to deal. That left it between LAL and Boston. Minnesota (McHale) chose Boston's trade package over LAL largely because Big Al had proved himself much more so than Andrew Bynum. I mean, who would you pick? The 20-11 big man or the 7ppg 5rpg big man? Bynum was too big of an unknown at that point and Odom was not a franchise cornerstone. Big Al was the best young talent on the table and Minnesota went for him.
If McHale didn't screw up, he could've had the 2007 draft pick (#5) that landed Ray Allen as well as Big Al. But he was hesitant and blew his opportunity. Ended up with a lesser deal.
......
So no KG wasn't as hyped to Boston for years before. It was more of a pipe dream that Boston didn't have the assets to get into. Then they did after an injury hit 2007 and the breakout of Big Al and suddenly Boston were prime trade destination. From then on, they were heavily named for KG.
That is my memory of it.