Alonso, 26, enjoyed a superb spell at Stamford Bridge last season, playing 30 Premier League games as the Blues stormed to the title.
But despite his impressive performances, Conte is keen to bolster his defensive options this summer ahead of Chelsea’s return to the Champions League.
The former Italy boss is an admirer of Juventus’ Alex Sandro, who is valued at over £60million, and is said to be hoping to bring him to the English capital.
The Premier League champions have also been linked with Southampton’s Ryan Bertrand but Alonso says he will fight for his place in the starting XI.
Chelsea's pre-season fixtures
Chelsea 3-0 Arsenal
Chelsea 2-3 Bayern Munich
July 29 – Inter Milan (Singapore – International Champions Cup)
Aug 6 – Arsenal (Wembley – Community Shield)
‘This is Chelsea – we play in four competitions this year,’ the Spanish defender told the Evening Standard.
‘We have so many games and competition can only be good for me and for the team. That’s it.
‘I will just keep training, keep improving, keep trying to do well for the team and keep fighting.’
Chelsea have already spent over £125m this summer while Manchester City’s spending passed £200m following Benjamin Mendy’s arrival at the Etihad.
‘It’s been a crazy summer. Teams are spending big money,’ 26-year-old Alonso added.
‘Compared to other years. It’s getting more and more expensive with time. If they have the money they can do whatever they want.
Alex Sandro has emerged as a target for the Premier League champions (Picture: Getty)
Neymar storms out of Barcelona training after fight with teammate
Manchester City waiting for Alexis Sanchez with 'open arms'
Wenger reveals his plan for Arsenal wonderkid after Emirates Cup inclusion
‘We need to be ready to play against every team. We are Chelsea. We will have to fight for every competition.’
As well as targeting a full back, Conte is also eyeing moves for Arsenal winger Alex Oxlade-Chamberlain and Everton star Ross Barkley.