But new boss Roy Hodgson laid down the law by telling the duo to ignore any rumours linking them with moves away from Anfield.
And Hodgson followed up his defiant stance by persuading Cole, a free agent after leaving Chelsea, to sign a four-year deal — much to the delight of Carragher.
The 32-year-old defender said: "It's great news and a message that Liverpool mean business.
"We have signed a top international player who has been really important for Chelsea.
"A lot of clubs wanted to sign him but it is a real coup he has chosen to come here and you have got to give the manager and the board a pat on the back for convincing him.
"Every supporter that I have spoken to is absolutely delighted and all the players are the same — it's given everyone a boost, just at the right time.
"It has been a long summer and we have been in a transitional period but now the World Cup is out of the way, we can start to look forward again.
"The fact we have got him has given everyone a boost around the city.
"It's good news again and, hopefully, there will be more to come. It's the kind of signing we needed to make."