An update version of WordPress is available.

You cannot update because WordPress 3.2.1 requires PHP version 5.2.1 or higher. You are running version 4.4.9.

While your sire is being updated, it will be in maintenance mode. As soon as you updates are complete, your sire will return to normal.

I’ve fixed this issue by simple command. In administration of my webhosting provider I’ve writen .php in space, which used to be blank (red rectangle). Files of .php are now executed under version of PHP 5.3 .

My webhosting provider is websupport.sk. But I am sure this simple trick will be working everywhere. Even when it looks little bit confusing it works. Upgrade was succesfull.

Additional information
If I delete .php from PHP 5.3 row after successfull installation, I get message on my blog:

Your server is running PHP version 4.4.9 but version 3.2.1 requires  at least 5.2.4

If it is working, it is O.K.  ;D

After hour of surfing over internet and looking for right answer I figure it out. Whole problem was just in wrong password for connection with database on side of my webhosting. Since I am using special characters, capital letters and numbers and have installed 2 different keyboards (EN,SK), when there is ************** security in typing the password I can not be never so sure what I am exactly writing.

When you have same problem during installation as me I suggest you to look up and check if password in wp-config.php is same as password for connection with database on your web-hosting provider.