The Spaniard has struggled at times during the 2018-19 campaign, with a switch to accommodate Maurizio Sarri's style of play meaning the full-back's performances have fluctuated.
The 28-year-old was in the Premier League team of the season under his previous manager Antonio Conte but has found it difficult to find consistency under Sarri, with Emerson Palmieri having been preferred in the left-back role at times.
And while he admits to being happy to remain at Stamford Bridge, he has left the door open to a potential exit. He said: "There is always talk [about a possible transfer].
"Yes [he is happy to hear of interest from Real Madrid]. It means I’m doing well if other teams are trying to get in touch. I am very happy here but we will see what happens this summer.
"First of all, I’m focussing on the final. I am very happy to have four more years here and hopefully I will stay many more years. For me, the path changed. I started very well. Then the manager wanted different things from me.
"After that, I was trying to do what he wanted and then he told me he wanted to play like I was at the beginning of the season. So maybe that has conditioned a little bit the way of my game. I think I’m settled now. I am very happy at Chelsea and looking forward to finishing the season with a win and a cup.
"It’s been a tough season, to be honest. We have lost important games at some points, but we have also won some games against big teams when we were struggling. For example, we beat the Champions League finalists [Tottenham] and we won against Manchester City at home.
"There have been too many ups and downs, we need more consistency."
There are times when Chelsea fans have turned on Alonso during the 2018-19 campaign, although despite being forced to turn off the comments on his Instagram account, he denies that harsh criticism from supporters have affected his game.
"Football is like this," he added. "The better the team you play for, the more fans follow you and there are millions of coaches and managers around the world! Some of them understand football one way; some of them have another opinion.
"I am the best to judge when I play well and when I don’t. Of course during the season you play some bad games, but it’s been a good campaign. I’m always looking for more, looking to improve and get better. That’s something inside me, I know I have to work for it.
"I don’t really care about the critics or when people talk good about me. It can’t affect you. I’m one to trust myself and to look for more. I had a good season and hopefully the next one will be even better."
Chelsea, who face Arsenal in the Europa League final on May 29, will be hoping to cut the 26-point gap to Manchester City next season and, should their two-window transfer ban go through, Alonso suspects some of the crop of loan players could be called upon to help out.
"That is the standard of the Premier League these days," he added. "Everyone is competing very well. They have built very good teams and there is a lot of competition. We want to win a trophy, even if Manchester City are winning or not.
"We have to think about ourselves, our fans and our families and give them a big satisfaction with a win. Sometimes it is only the small details that make the difference in one season. We have to keep the concentration for the whole season, take our chances to score the goals, defend well as a team.
"There are so many things we have to focus on for the whole season. It is not easy but that is what we have to aim for. We have a lot of players and a lot of quality in the team, also lots of players on loan who can help [in the event of a transfer ban].
"We will see what happens, but I trust this team and we have been doing very good things in the last two or three years and we will fight to keep that position."