Alonso signed an extension at the Santiago Bernabeu on Wednesday that will keep him in Madrid until 2016, with his original deal having been due to expire at the end of the current campaign.
The former Liverpool man was linked with a host of clubs in the Premier League but stated on Friday that no offers had been put to him.
"I haven't received any offers that I know of. I spoke a lot with Alvaro Arbeloa and my team-mates who all asked me to stay," he said.
"I'm very grateful for the love the Bernabeu gives me. The fans have always showed me their love and support.
"I wanted to make sure that my family and I are happy to be in Madrid. This is the best place for me."
Alonso, who is currently sidelined with a perforated eardrum, added that his relationship with coach Carlo Ancelotti had a major influence on his decision to stay at Madrid.
"I've had a great relationship with (Manuel) Pellegrini, (Jose) Mourinho (Real's last two coaches) and now with Ancelotti. I'm here to help the team.
"My relationship with Ancelotti played an important role in my decision to renew the contract.
"It has been a process; I needed to make sure that I can be at 100 per cent in order to make a decision.
"I still have the same role in the team. I want to win the Champions League with Real Madrid."
