Alonso started his role as Chelsea boss this month as he prepares to manage a side who finished 10th in the Premier League last season despite mass spending and countless world-class players.
The former midfielder led Bayer Leverkusen to the Bundesliga title before joining Real Madrid and being sacked due to a lack of patience from the board regarding poor results.
With no European football in the new season, Alonso will have plenty of time to work with the squad next season, allowing him to shape the side how he wants.
Speaking to BetBrothers, Monreal revealed that the Blues must allow Alonso time to turn the team around and cannot expect immediate results.
"It's a big job for Xabi Alonso. It's a big responsibility. I think he's a really good manager, but my only concern is he needs time. If Chelsea gives him time, he's going to do it really well.
"But in football, most clubs want results from the first day. And it's going to be a big challenge for Xabi Alonso to do that.
"For example, in Real Madrid he was doing a good job, but they didn't wait for him. In the first moment they had the opportunity to sack him. They did it.
"Chelsea have a good team, really, really good players. Are they a threat to Arsenal? Yes, of course. If you see Chelsea's squad, you realise immediately that they have a really good team.
"We don't know what will happen, but they can be a threat. Manchester United, Manchester City, Chelsea, anyone can be a threat, but I think Arsenal right now, is one step in front of the rest, without a doubt."
Brighton will visit Stamford Bridge for Alonso's home debut as Blues boss following the opening clash with Fulham next month where fans cannot expect instant results.