Pietersen was dropped for the Lord's Test against South Africa in August and overlooked for the World Twenty20 following allegations he sent messages to Proteas players criticising then England captain Andrew Strauss.
After a stand-off period, the 32-year-old apologised for sending the messages and signed a new ECB central contract after agreeing to enter a "re-integration" process with the team.
Pietersen will shortly meet up with his England team-mates and coach Andy Flower as they bid to rebuild bridges, and Broad is hopeful there will be a positive outcome to those talks, telling the BBC: "It's in the management's hands. Of course (we'd welcome him back). We've had some amazing success with KP as a team."
He added: "I've been in the side six years, we've won two Ashes series and a Twenty20 World Cup, and we know that KP is a really dangerous player for us.
"There's not a better man in charge than Andy Flower to put the situation right and there's a lot of trust in him at the moment.
"Whether it's for (the tour of) India or New Zealand, the team will welcome him back.
"We pride ourselves on being an honest changing room and the only way to move forward is to talk about things.
"There will be a meeting with some of the hierarchy and we just need to lay some things out.
"I think that will be a really good meeting with most of the England players, and hopefully we can move forward and draw a line under the whole experience."
- Andy Flower