Quiero solicitar un permiso.

After querer when you say you want to do something, the next verb stays in the infinitive.

• Quiero solicitar = I want to apply/request
• Quiero comer = I want to eat
• Quiero hablar = I want to speak

So quiero solicito is incorrect because solicito is a conjugated form, and after quiero you normally need the infinitive: solicitar.

In Spanish, subject pronouns are often omitted because the verb ending already shows who the subject is.

• quiero already means I want
• so yo quiero is possible, but usually unnecessary

You would add yo only for emphasis, contrast, or clarity:

• Yo quiero solicitar un permiso, pero ella no.
  I want to request leave, but she doesn’t.

So Quiero solicitar un permiso is completely natural.

Quiero is the first-person singular present tense of querer.

The full present-tense pattern is:

• yo quiero
• tú quieres
• él/ella quiere
• nosotros queremos
• vosotros queréis
• ellos/ellas quieren

This verb is stem-changing: e → ie in most forms.

That is why it is quiero, not quero.

Both can mean to ask for or to request, but they are not used in exactly the same way.

• solicitar is usually more formal
• pedir is more general and common in everyday speech

Examples:

• solicitar un permiso = to formally request leave / a permit
• pedir ayuda = to ask for help
• pedir un café = to order a coffee

In Spain, solicitar un permiso sounds quite appropriate in a workplace, administrative, or official context.

Permiso can mean different but related things depending on context:

• permission
• permit
• leave from work
• official authorization

In a sentence like solicitar un permiso, it often suggests something formal, such as:

• asking for leave from work
• requesting authorization
• applying for a permit

So permiso is broader than just the English word permission.

Here, permiso is being treated as a countable noun, so Spanish normally uses an article.

• un permiso = a permit / a period of leave / a request for authorization
• el permiso = the permit / the leave / the authorization

Spanish often uses articles where English sometimes does not.
So solicitar un permiso sounds natural because it means requesting a specific permission/permit/leave.

Yes, it sounds fairly formal or neutral-formal.

• solicitar is the main reason it sounds formal
• the structure is suitable in work, HR, legal, or administrative situations

In more casual speech, someone might say:

• Quiero pedir un permiso
• Quiero pedir permiso
• Necesito pedir un día libre

So the original sentence is correct and natural, especially in official contexts.

Yes, but it is not exactly the same.

• pedir permiso usually means to ask for permission
• solicitar un permiso often sounds more official, like requesting a permit, leave, or formal authorization

So:

• Quiero pedir permiso = I want to ask for permission
• Quiero solicitar un permiso = I want to formally request a permit / leave / authorization

In many situations they may overlap, but the tone is different.

A simple Spain Spanish pronunciation guide is:

KYEH-ro so-lee-see-TAR oom pehr-MEE-so

A few points:

• qui in quiero sounds like kye
• the r in quiero is a light tap
• c in solicitar before i is pronounced th in most of Spain, so it sounds like soli-thi-TAR
• un permiso may sound a bit connected in fast speech

A more Spain-like approximation would be:

KYEH-ro so-lee-thee-TAR um pehr-MEE-so

Often, yes. Me gustaría sounds more polite and less direct.

Compare:

• Quiero solicitar un permiso = direct, clear
• Me gustaría solicitar un permiso = more polite, softer
• Quisiera solicitar un permiso = also polite, slightly formal

In a workplace or email, many speakers would prefer:

• Me gustaría solicitar un permiso
• Quisiera solicitar un permiso

But Quiero solicitar un permiso is still grammatically correct.