Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
Carroll is currently on a season-long deal at Upton Park from parent club Liverpool, who host the Hammers in the Barclays Premier League on Sunday.
The 24-year-old will be unavailable for the clash at Anfield due to the terms of his loan deal and has scored only five times since moving to east London last summer.
But Demel wants the England international to extend his stay at West Ham.
"Andy is a really good player and beyond that he is a really good man," he told Press Association Sport.
"I didn't know him before he signed for West Ham but to see a young player with the amount of pressure he had and the way he has behaved, I'm really happy to be his team-mate and I'd be really pleased if he stayed and played for West Ham."
Liverpool splashed out £35million on Carroll to take him from hometown club Newcastle in January 2011 as they looked to re-establish themselves in the top four of the Premier League.
Despite signing the likes of Carroll, Luis Suarez, Jordan Henderson and Stewart Downing the Reds have struggled to fight the likes of Manchester City, Manchester United and Chelsea but Demel is still expecting a tough task.
"It is still Anfield, it is still Liverpool," he added. "They won't be easy to beat and it won't be easy to play there even if they aren't the great Liverpool.
"They still have really good players in the squad who are capable of making a difference so we just have to focus on the basics and play our best."
West Ham started the season well after manager Sam Allardyce took them back to the top flight at the first time of asking.
A slump around Christmas plus a poor run of results of late mean they have fallen into the bottom half of the table. Allardyce reckons 38 points will be enough to achieve survival and last weekend's 3-1 win over West Brom took the Hammers to within two points of that total.
Demel agrees that the club are close to securing a second season of Premier League football but insists their end-of-year targets remain higher than purely surviving.
"The game against West Brom was really important," he said.
"We needed the three points because this coming week we are going to Liverpool and we had lost some points over the last few games.
"We are going to Liverpool and we will be trying to get at least one point to keep things going. It is now the last phase of the season and every point is important.
"First of all we need to be safe but then we can try and finish 10th - it is like progression, this is what we are looking for."
West Ham have taken 11 of their 36 points away from home so far and Demel feels home form is vital for a teams who are newly-promoted.
"When you are in the situation we are in I think it is important to win your games at home," he said.
"We have good form at home and in front of our fans and at our stadium we have improved and I think away from home we have had some bad luck - some results we didn't deserve."
Establishing themselves as a top-flight club has become all the more important for West Ham after it was announced last month that they will become anchor tenants of the Olympic Stadium from the start of the 2016 season.
Demel, whose current contract runs until 2015, hopes to be involved once the move has taken place and believes it is a necessity if the club are to progress.
"Everyone knows West Ham will get a new stadium in 2016 and it would be nice to improve year after year and, by then, have a really good team to compete for first place in the Premier League," he said.
"I know how important it is for the club to move to a bigger stadium, for the fans as well, for the future.
"I think everyone will be happy - the facilities will be there and a club like West Ham needs to have a big stadium. We have a lot of good fans who support the team all the time."